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% File: portable.tex

% Contents:
% Portable and Efficient Constructs chapter for HPF 2.0 document,
% including 
%	Kernel HPF
%	FORALL examples

% Revision history:
% May-10-96	Created by Andy Meltzer, Cray Research
%		(who thought it was ``Kernel HPF'')



\chapter{Portable and Efficient Constructs}
\label{ch-portable}


{\em
Comments on this chapter should be directed to 
Andy Meltzer ({\tt meltzer@cray.com}),
Chuck Koelbel ({\tt chk@cs.rice.edu}),
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Portable/Efficient}'' as the {\tt Subject:}
line.
\par
}



%  {Coding for Portable Performance in HPF}
%  {Ver 1.0}
%  {Andrew Meltzer}
%  {Cray Research, Inc.}
%  {April, 1996}


%\section{Introduction}


This chapter identifies a specific set of directives
and paradigms that are particularly easy to use.  This set compiles to an
efficient parallel program on the vast majority of platforms available.  The
aim of the chapter is to identify a set of features that will provide
portable high performance.

HPF 2.0 includes many features that offer ease of use, but
the excessive overhead associated with the implementation of these features
can severely
compromise performance on one or more (even all for some combination
of features) distributed memory parallel computers.  This ``Kernel'' set
of features, often referred to as the {\em HPF Kernel} is described in this
chapter.

The HPF Kernel is a high performance subset of HPF 2.0.  The features chosen
for were selected for the following reasons
\begin{itemize}
\item They allow high-performance across all platforms.
\item On no platform are there performance ``surprises,''  Few, if any,
      combinations
      of the portable, high-performance features unexpectedly lead
      the user into low-performance
      circumstances although it is still possible for application
      programmers to write low-performance codes and for vendors to
      provide low-performance implementations.
\item They are easily understood.
\item They are commonly used.
\item They are valuable for all platforms.
\end{itemize}

The features described in this chapter are also chosen to
simplify the HPF model by reducing the variety of mappings to
only those most commonly used and to simplify
the model by removing a level of abstraction.  These kernel features
might be a good place to begin learning to program in HPF.

The use of these features does not guarantee a high-performance application,
but these features increase the likelyhood that an application will get the
most out of the HPF language.   These features are also described here to
assist the user with an understanding of the sorts of operations that can
be efficiently executed.  Many vendors will have implemented many more
features that execute efficiently, a description of these is available
with the vendor's implementation.

The chapter is organized by HPF feature.  Features are listed and described
as restricted, not recommended, or recommended.   Restrictions are described.

\section{The {\tt {DISTRIBUTE}} Directive}

The {\tt {DISTRIBUTE}} directive remains mostly intact, only a few pieces
of functionality are not suggested when trying to achieve portable performance.
\subsection{Distribution Formats}

The HPF Kernel includes only the {\tt {BLOCK}} and {\tt {CYCLIC}} and
on-processor distributions.  It does
not include the {\tt {CYCLIC(N)}}, or {\tt {BLOCK(N)}}
distributions.  The effort to determine the locations of the elements
in an array with the {\tt {BLOCK}} and {\tt {CYCLIC}} distribution
is much less than the parameterized distributions.

\subsection{On-Processor Dimensions}
The ``*'' syntax is included in the {\tt {DISTRIBUTE}} directive
{\em {dist-format-clause}} to indicate on-processor dimensions.

This is a convenient technique for increasing locality of
reference, a goal for most high performance codes.  It can be accomplished
efficiently with reasonable compiler effort.

\section{\tt {DYNAMIC} Distributions}

The {\tt {DYNAMIC}} attribute is not recommended for portable
high-performance coding.   These distributions have obvious merit and
certain applications may require their general capabilities,  but
because of the inherent dynamic overhead required on even the most
advanced implementations, they cannot be recommended as high-performance
features.

\section{The {\tt {PROCESSORS}} Directive}

The {\tt {PROCESSORS}} directive is part of the HPF Kernel
with the following restrictions:
\begin{itemize}
\item The product of the extents must exactly match the number of
      processors or the processor arrangement must be scalar.
\item If an {\tt {ONTO}} clause is not specified, a default
      arrangement is provided which is identical for distributees
      that have identical shapes and identical explicit mappings.
\end{itemize}

If a processors directive is not specified a default arrangement is
provided which is identical for arrays that have identical shapes,
bounds, and identical explicit mapping directives.


\section{The {\tt {ALIGN}} Directive}

In The HPF Kernel the {\tt {ALIGN}} directive is restricted to
alignments that are direct;  there may be no offsets or strides
within an  {\tt {ALIGN}}.
Replication and collapse of dimensions is allowed.
In alignment expressions the dimensions may not be permuted.

\begin{itemize}
\item   Alignments may not contain offsets or strides.
\item   The {\em {align-subscript-use}} in the HPF 1.1 syntax rules should be
        replaced with {\em {align-dummy}}.

\item   Dimensions may not be permuted.

\item   A `*' is allowed either in the align-spec or in the alignee.
\end{itemize}

For example the following is code will likely execute efficiently:

        {\tt {CHPF\$           ALIGN A(I,J) WITH B(I,J)}}

But the following may not:

        {\tt {CHPF\$           ALIGN A(I,J) WITH B(I+1,J)}}


Offsets are not suggested for the {\tt {ALIGN}} directive when coding
for portable high-performance.  The effect of offsets can be
often be achieved by changing the bounds of arrays.
The following two examples will create the same alignment.

    {\em {Example 2a}}
\begin{verbatim}
                DIMENSION A(1:100), B(0:99)
        CHPF$   PROCESSORS P(32)
        CHPF$   DISTRIBUTE B(BLOCK) ONTO P
        CHPF$   ALIGN A(I) WITH B(I-1)  ! Disallowed
\end{verbatim}

    {\em {Example 2b}}
\begin{verbatim}
                DIMENSION A(1:100), B(0:99)
        CHPF$   PROCESSORS P(32)
        CHPF$   DISTRIBUTE A(BLOCK) ONTO P
        CHPF$   DISTRIBUTE B(BLOCK) ONTO P
\end{verbatim}

\section{The {\tt {TEMPLATE}} Directive}

The {\tt {TEMPLATE}} directive itself needs no restriction, but the use of
templates is restricted by the changes to the {\tt {ALIGN}} directive.


\section{The Reduction Clause in the {\tt INDEPENDENT} Directive}

The reduction clause in the {\tt INDEPENDENT} directive
may be used when coding for portable
high-performance.  The directive
only pertains to intrinsic operators and types.

\section{The {\tt {FORALL}} Statement and Construct}

Both the {\tt FORALL} statement and construct are recommended for
use when coding for portable high-performance.

{\tt {FORALL}} is a powerful and expressive way
to code parallelism.  It is true that not all {\tt {FORALL}}
statements and/or constructs can be fully parallelized, but because
of their general value and because they will be part of Fortran 95,
they are included in the HPF Kernel.

\section{{\tt {PURE}} Functions and Subroutines}

These are recommended for use when coding for portable high-performance.
{\tt {PURE}} functions can do no harm, and allow
an increased level of expressiveness.  They simplify the job for
the compiler and are part of Fortran 95.

\section{The {\tt {INDEPENDENT}} Directive}

The {\tt {INDEPENDENT}} directive is recommended for portable
high-performance, but with some caveats.  The {\tt {INDEPENDENT}}
directive gives a user access to facilities otherwise not available
by any means.  It can be abused, however, and not all implementations
may be able to handle all combinations of function calls within
{\tt INDEPENDENT} loops.  Care must be taken when exploiting this
feature.

Directives such as {\tt {INDEPENDENT}} have shown
their worth historically across a broad variety of platforms.  This
directive simplifies the analysis the compiler must do and can inform
the compiler about optimizations that it may do that otherwise
are expensive or impossible to deduce.   {\tt {INDEPENDENT}} allows
an increased level of optimization.

\section{Extrinsics and {\tt {HPF\_LOCAL}} and {\tt {HPF\_SERIAL}} }

The general purpose extrinsic mechanism, {\tt {HPF\_LOCAL}} and
{\tt {HPF\_SERIAL}} are all recommended for use when coding for
portable high-performance.

These allow a program to get at the highest performing features of a
particular architecture.


\section{Library}

All of the HPF 1.1 library routines are recommended for use when
coding for portable high-performance.  The intrinsics provide fast,
architecture specific
versions of many very important parallel functions.  To achieve a
similar level of performance for these functions a user would have
to write non-portable code.


\section{The {\tt {INHERIT}} Directive}

The  {\tt {INHERIT}} directive is recommended for use when coding
for portable high-performance.
The {\tt {INHERIT}} directive is not a high-performance
feature, but its impact can be isolated to the few places where it is
very useful.  The {\tt {INHERIT}} directive can be instrumental when
coding library and general purpose routines.

Care must be taken when using this directive as it is only a convenience
feature, not a high-performance feature.


\section{Pointers}

When coding for portable high-performance it is recommended that a
given pointer only point to identically explicitly mapped objects.


\section{Subroutine Interfaces}

Explicit interfaces are recommended for any subroutine
which remaps data.  This gives the language processor the necessary
means (without interprocedural optimizations) to remap data at
the call site statically, rather than dynamically at the callee.
Dummy arguments from actual argument array sections cannot be
mapped ``{\tt {DISTRIBUTE * ONTO *}}.'' Non-unit
strides may be specified when passing array sections as actual
arguments.

Assumed shape explicitly mapped dummies  may be used,
but explicit interfaces must be included where ever
they are used. Assumed shape dummies may use any mapping syntax.
The results of array valued functions may be explicitly mapped.  Assumed
size arrays are not recommended.

An explicit interface is required in the following cases:

\begin{itemize}

\item The dummy argument has the {\tt {INHERIT}} attribute.
\item  The mapping of a dummy argument is not the same as the mapping of
the corresponding actual argument, and at least one of the following
two conditions is true:

\begin{enumerate}
        \item the dummy argument is explicitly mapped;

        \item the actual argument is an explicitly mapped whole array or
           a section of an explicitly mapped array.
\end{enumerate}

\end{itemize}



Much better control of the remapping can be achieved
if the explicit interface is available and much less code to check
mappings and remap upon entry is necessary.

\section{Storage and Sequence Association}

It is not recommended that storage or sequence association be relied
upon when coding for portable performance.
The {\tt SEQUENCE} directive is not suggested.  This means that the user
should not use equivalence, common blocks must be declared identically
everywhere, and no arguments may be passed with mismatched shapes.




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From owner-hpff-doc  Mon Aug  5 08:31:29 1996
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% File: mapping-subr.tex

% Contents:
% Mapping constructs for dummy arguments for HPF 2.0 document,
% including
%       interface rules
%       INHERIT
%       the rest of pointer mappings


% Revision history:
% Jun-03-96     First edit by Carl Offner, Digital.
%               (Rearrangements, many edits, and two new sections; see
%               the comments at the top of the chapter.)
% May-10-96     Created by Charles Koelbel, Rice University
%               (from HPF 1.2 document and HPF 2.0 proposals)

% If you don't have LaTeX2e available, uncomment the next three lines:
%\def\emph#1{{\em #1}}
%\def\texttt#1{{\tt #1}}
%\def\textit#1{{\it #1}}



\chapter{Data Mapping in Subprogram Interfaces}
\label{ch-mapping-subr}

{\em
Comments on this chpater should be directed to 
Piyush Mehrotra ({\tt pm@icase.edu}), 
Carl Offner ({\tt offner@hpc.pko.dec.com}), 
Guy Steele ({\tt Guy.Steele@east.sun.com}),
and \\
{\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Mapping in Subprogram Calls}'' as the
{\tt Subject:} line.
\par
}


\emph{In this chapter, phrases such as ``it is the responsibility of
  the subprogram to remap the argument'' are constraints on the
  implementation (i.e., on the generated code produced by the
  compiler), not on the source code produced by the programmer.}



\section{Introduction}
\label{mapsub:introduction}

\emph{This introduction gives an overview of the ways in which mapping
directives interact with argument passing to subroutines.  The
language used here, however, is not definitive; the subsequent
sections of this chapter contain the authoritative rules.}

In addition to the data mapping features described in
Chapter~\ref{ch-mapping-base}, HPF allows a number of options for
describing the mapping of dummy arguments to subprograms.

The mapping of each such dummy argument may be related to the mapping
of its associated actual argument in the calling routine (the
``caller'') in several different ways.  To allow for this, mapping
directives applied to dummy arguments can have three different
syntactic forms: \emph{prescriptive}, \emph{descriptive}, and
\emph{transcriptive}.

HPF provides these three forms to allow the programmer either to
specify that the data is to be left in place, or to specify that
during the execution of the call to the subroutine the data must be
automatically remapped into a new and presumably more efficient mapping
for the duration of the subprogram's execution.

The meaning of these forms is as follows:

\begin{description}
  
\item[prescriptive] The directive describes the mapping of the dummy.
  However, the actual as passed may not have this mapping.  \emph{If
  it does not}, it is the responsibility of the subprogram to remap
  the argument as specified, and to restore the original mapping on
  exit.  (However, see the discussion on explicit interfaces and
  remapping below.)

  Prescriptive directives are syntactically identical to directives
  occurring elsewhere in the program.  For instance, if \texttt{A} is
  a dummy argument,

                                                                \CODE
!HPF$ DISTRIBUTE A (BLOCK, CYCLIC)
                                                                \EDOC
  is a prescriptive directive.
  
\item[descriptive] The directive describes the mapping of the dummy.
  It is the responsibility of the calling routine to insure that the
  actual as passed has this mapping.  (Similarly, remapping to restore
  the original mapping on exit is also done by the caller.)

  Descriptive directives look like prescriptive directives, except
  that an asterisk precedes the description.  For instance,
                                                                \CODE
!HPF$ DISTRIBUTE A *(BLOCK, CYCLIC)
                                                                \EDOC
  is a descriptive directive.

\item[transcriptive] The mapping is unspecified.  The called subroutine
  must accept the mapping of the argument as it is passed.  (Of course
  this means that the caller must pass this mapping information at
  run-time.)
  
  Transcriptive directives are written with a single asterisk for 
  distributions and processor arrays; for instance
                                                                \CODE
!HPF$ DISTRIBUTE A *
                                                                \EDOC
  is a transcriptive directive.  The \texttt{INHERIT} directive
  (see Section~\ref{INHERIT-SECTION}) is used to specify a transcriptive
  alignment.

\end{description}

Both distributions and processor arrangements can be specified to be
prescriptive, descriptive, or transcriptive.  Alignment is more
complicated, because of the need to specify the template to which the
dummy is aligned.  This template may be unspecified (in this case of
course there is no \texttt{ALIGN} directive), in which case it is the
\emph{natural template} of the dummy.  (``Natural template'' is
defined in Section~\ref{mapsub:templates} below.)  Otherwise, one of
the following disjoint possibilities must be true:

\begin{itemize}

\item The template is explicitly specified by a prescriptive ALIGN directive.

\item The template is explicitly specified by a descriptive ALIGN directive.
  
\item The template is \emph{inherited}.  This is specified by giving
  the dummy the \texttt{INHERIT} attribute (described in
  Section~\ref{INHERIT-SECTION} below).  This implicitly specifies
  the template to be the template with which the corresponding actual
  argument is ultimately aligned; further, the alignment of the dummy
  with that template is the same as that of the corresponding actual.
  This is in effect a transcriptive form of alignment.

\end{itemize}

This is restated more precisely in Section~\ref{mapsub:templates}
below.

If remapping is necessary at a procedure interface, this fact must be
visible in the caller.  This is a consequence of the requirements for
explicit interfaces in Section~\ref{mapsub:ExplicitInterfaces}.

As a result of this, an implementation may choose to have all
necessary remapping done by the caller.  This in effect eliminates the
distinction between prescriptive and descriptive mappings, and
eliminates the need for the descriptive form of the directives.

While both prescriptive and descriptive syntactic forms remain in this
document, and while they are each treated in this Chapter, it is fair
to say that the descriptive syntax is at this point maintained for
backwards compatibility, and is primarily of historic interest.

\begin{users}
  Although it is possible to write some combinations of mapping
  directives that are partially prescriptive and partially
  transcriptive, for instance, there is probably no virtue to so
  doing.  The point of these directives is to enable the compiler to
  handle any necessary remapping correctly and efficiently.  Now
  remapping can happen for one or more of the following reasons:

  \begin{itemize}
  \item  to make the alignment of the actual and the dummy agree;
  \item  to make the distribution of the actual and the dummy agree;
  \item  to make the processor array of the actual and the dummy agree.
  \end{itemize}

  For most machines, there is no real difference in the cost of
  remapping for any of these reasons.  It is therefore a better
  practice in general to make a mapping either purely transcriptive,
  purely prescriptive, or purely descriptive.

  While transcriptive mappings can be useful in writing libraries,
  they impose a run-time cost on the subprogram.  They should
  therefore be avoided in normal user code.
\end{users}

\section{What Remapping is Required, and Who Does It}

If there is an explicit interface for the called subprogram and that
interface contains prescriptive or descriptive mapping directives for
a dummy argument, and if a remapping of the corresponding actual
argument is necessary, the call should proceed as if the data was
copied to a temporary variable to match the mapping of the dummy
argument as expressed by the directives in the explicit interface.
The template of the dummy will then be as declared in the interface.

If in such a case, the mapping directives are descriptive, then it is
the responsibility of the caller to perform the necessary remapping.
That is, the caller must provide an actual argument matching such
directives, so that the descriptive directives correctly describe the
dummy arguments to the subprogram.

\begin{implementors}
In fact, an implementation may choose to have \emph{all} necessary
remapping done by the caller.
\end{implementors}

If there is no explicit interface, then no remapping will be
necessary; this is a consequence of the requirements in
Section~\ref{mapsub:ExplicitInterfaces}.

An overriding principle is that \emph{any remapping of arguments is
not visible to the caller}.  That is, when the subprogram returns and
the caller resumes execution, all objects accessible to the caller
after the call are mapped exactly as they were before the call.  It is
not possible for a subprogram to change the mapping of any object in a
manner visible to its caller.

\section{Distributions and Processor Arrangements}
\label{mapsub:DistProcArr}

In a \texttt{DISTRIBUTE} directive where every \textit{distributee} is
a dummy argument, either the \textit{dist-format-clause} or the
\textit{dist-target}, or both, may begin with, or consist of, an
asterisk.

\begin{itemize}
  
\item Without an asterisk, a \textit{dist-format-clause} or
  \textit{dist-target} is prescriptive; the clause describes a
  distribution and constitutes a request of the language processor to
  make it so.  This might entail the subprogram remapping or copying
  the actual argument on entry at run time in order to satisfy the
  requested distribution for the dummy.
  
\item Starting with an asterisk, a \textit{dist-format-clause} or
  \textit{dist-target} is descriptive; the clause describes a
  distribution and constitutes an assertion to the language processor
  that on entry to the subprogram it will already be so.  The
  programmer claims that, for every call to the subprogram, the actual
  argument will be such that the stated distribution already describes
  the mapping of that data.  (The intent is that if the argument is
  passed by reference, no movement of the data \emph{by the
  subprogram} will be necessary at run time.  All this is under the
  assumption that the language processor has observed all other
  directives.  While a conforming HPF language processor is not
  required to obey mapping directives, it should handle descriptive
  directives with the understanding that their implied assertions are
  relative to this assumption.)

\item Consisting of only an asterisk, a \textit{dist-format-clause} or
  \textit{dist-target} is transcriptive; the clause says nothing about
  the distribution but constitutes a request of the language processor
  to copy that aspect of the distribution from that of the actual
  argument.  (The intent is that if the argument is passed by
  reference, no movement of the data will be necessary at run time.)
\end{itemize}

It is possible that, in a single \texttt{DISTRIBUTE} directive, the
\textit{dist-format-clause} might have an asterisk but not the
\textit{dist-target}, or vice versa.

\subsection{Examples}

These examples of \texttt{DISTRIBUTE} directives for dummy arguments
illustrate the various combinations:

                                                                        \CODE
!HPF$ DISTRIBUTE URANIA (CYCLIC) ONTO GALILEO
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{URANIA} to have a \texttt{CYCLIC} distribution on the
processor arrangement \texttt{GALILEO}.
                                                                        \CODE
!HPF$ DISTRIBUTE POLYHYMNIA * ONTO ELVIS
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{POLYHYMNIA} to be distributed onto the processor arrangement
\texttt{ELVIS}, using whatever distribution format it currently has
(which might be on some other processor arrangement).
                                                                        \CODE
!HPF$ DISTRIBUTE THALIA *(CYCLIC) ONTO FLIP
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{THALIA} to have a \texttt{CYCLIC} distribution on the
processor arrangement \texttt{FLIP}; \texttt{THALIA} already has a
cyclic distribution, though it might be on some other processor
arrangement.
                                                                        \CODE
!HPF$ DISTRIBUTE CALLIOPE (CYCLIC) ONTO *HOMER
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{CALLIOPE} to have a \texttt{CYCLIC} distribution on the
processor arrangement \texttt{HOMER}; \texttt{CALLIOPE} is already
distributed onto \texttt{HOMER}, though it might be with some other
distribution format.
                                                                        \CODE
!HPF$ DISTRIBUTE MELPOMENE * ONTO *EURIPIDES
                                                                        \EDOC
\texttt{MELPOMENE} is asserted to already be distributed onto
\texttt{EURIPIDES}; use whatever distribution format the actual
argument had so, if possible, no data movement should occur.
                                                                        \CODE
!HPF$ DISTRIBUTE CLIO *(CYCLIC) ONTO *HERODOTUS
                                                                        \EDOC
\texttt{CLIO} is asserted to already be distributed \texttt{CYCLIC}
onto \texttt{HERODOTUS} so, if possible, no data movement should
occur.
                                                                        \CODE
!HPF$ DISTRIBUTE EUTERPE (CYCLIC) ONTO *
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{EUTERPE} to have a \texttt{CYCLIC} distribution onto whatever
processor arrangement the actual was distributed onto.
                                                                        \CODE
!HPF$ DISTRIBUTE ERATO * ONTO *
                                                                        \EDOC
The mapping of \texttt{ERATO} should not be changed from that of the
actual argument.
                                                                        \CODE
!HPF$ DISTRIBUTE ARTHUR_MURRAY *(CYCLIC) ONTO *
                                                                        \EDOC
\texttt{ARTHUR_MURRAY} is asserted to already be distributed
\texttt{CYCLIC} onto whatever processor arrangement the actual
argument was distributed onto, and no data movement should occur.

Also note that \texttt{DISTRIBUTE ERATO * ONTO *} does not mean the
same thing as
                                                                        \CODE
!HPF$ DISTRIBUTE ERATO *(*) ONTO *
                                                                        \EDOC
This latter means:  \texttt{ERATO} is asserted to already be distributed
\texttt{*} (that is, on-processor) onto whatever processor arrangement the
actual was distributed onto.  The processor arrangement is necessarily
scalar in this case.

\subsection{What Happens When a Clause is Omitted}

One may omit either the \textit{dist-format-clause} or the
\textit{dist-onto-clause} for a dummy argument.  This is understood as
follows:

If the dummy argument has the \texttt{INHERIT} attribute (see
Section~\ref{INHERIT-SECTION}), then no distribution directive is
allowed in any case:  the distribution as well as the alignment is
inherited from the actual argument.

In any other case in which distribution information is omitted, the
compiler may choose the distribution format or a target processor
arrangement arbitrarily.

Here are two examples:
                                                                         \CODE
!HPF$ DISTRIBUTE WHEEL_OF_FORTUNE *(CYCLIC)
                                                                         \EDOC
\texttt{WHEEL_OF_FORTUNE} is asserted to already be \texttt{CYCLIC}.
As long as it is kept \texttt{CYCLIC}, it may be remapped onto some
other processor arrangement, but there is no reason to.
                                                                          \CODE
!HPF$ DISTRIBUTE ONTO *TV :: DAVID_LETTERMAN
                                                                          \EDOC
\texttt{DAVID_LETTERMAN} is asserted to already be distributed
on \texttt{TV} in some fashion.  The distribution format may be
changed as long as \texttt{DAVID_LETTERMAN} is kept on \texttt{TV}.
(Note that this declaration must be made in attributed form; the
statement form

                                                                        \CODE
!HPF$ DISTRIBUTE DAVID_LETTERMAN ONTO *TV         !Nonconforming
                                                                        \EDOC
does not conform to the syntax for a \texttt{DISTRIBUTE} directive.)




\section{Alignment}

\subsection{The Template of the Dummy Argument}
\label{mapsub:templates}

Here we describe precisely how the template with which the dummy
argument is ultimately aligned is arrived at.

First, templates are not passed through the subprogram argument
interface.  The template to which a dummy argument is aligned is
always distinct from the template to which the actual argument is
aligned, though it may be a copy (see Section \ref{INHERIT-SECTION}).
On exit from a subprogram, an HPF implementation arranges that the
actual argument is aligned with the same template with which it was
aligned before the call.

Thus, a dummy argument always has a fresh template to which it is
ultimately aligned.  This template is constructed in one of three
ways:

\begin{itemize}
\item If the dummy argument appears explicitly as an \textit{alignee}
  in an \texttt{ALIGN} directive, its template is specified by the
  \textit{align-target}.
  
\item If the dummy argument is not explicitly aligned and does not
  have the \texttt{INHERIT} attribute (described in
  Section~\ref{INHERIT-SECTION} below), then the template has the same
  shape and bounds as the dummy argument; this is called the
  \textit{natural template} for the dummy.

  (Thus, all the examples in Section~\ref{mapsub:DistProcArr} use
  the natural template.)

\item If the dummy argument is not explicitly aligned and does have
  the \texttt{INHERIT} attribute, then the template is ``inherited'' from
  the actual argument according to the following rules:

  \begin{itemize}
    
  \item If the actual argument is a whole array, the template of the
    dummy is a copy of the template with which the actual argument is
    ultimately aligned.
    
  \item If the actual argument is an array section of array \(A\)
    where no subscript is a vector subscript, then the template of the
    dummy is a copy of the template with which \(A\) is ultimately
    aligned.

  \item If the actual argument is any other expression, the shape
    and distribution of the template may be chosen arbitrarily by
    the language processor (and therefore the programmer cannot know
    anything \textit{a priori} about its distribution).

  \end{itemize}
  
  In all of these cases, we say that the dummy has an \textit{inherited
  template} rather than a natural template.

\end{itemize}


\subsection{The INHERIT Directive}
\label{INHERIT-SECTION}

The \texttt{INHERIT} directive specifies that a dummy argument should be
aligned to a copy of the template of the corresponding actual argument
in the same way that the actual argument is aligned.

                                                                        \BNF
inherit-directive      \IS  INHERIT dummy-argument-name-list
                                                                        \FNB

The \texttt{INHERIT} directive causes the named subprogram dummy
arguments to have the \texttt{INHERIT} attribute.  Only dummy
arguments may have the \texttt{INHERIT} attribute.  An object must not
have both the \texttt{INHERIT} attribute and the \texttt{ALIGN}
attribute.  The \texttt{INHERIT} directive may appear only in a
\textit{specification-part} of a scoping unit.

If a dummy argument has the \texttt{TARGET} attribute and no explicit
mapping attributes, then the \texttt{INHERIT} attribute is implicitly
assumed.  (See section~\ref{mapsub:pointers}.)

The \texttt{INHERIT} attribute specifies that the template for a dummy
argument should be inherited, by making a copy of the template of the
actual argument.  Moreover, no other explicit mapping directive may
appear for an argument with the \texttt{INHERIT} attribute: the
\texttt{INHERIT} attribute implies a distribution of
\texttt{DISTRIBUTE~*~ONTO~*} for the inherited template.  Thus, the
net effect is to tell the compiler to leave the data exactly where it
is, and not attempt to remap the actual argument.  The dummy argument
will be mapped in exactly the same manner as the actual argument; the
subprogram must be compiled in such a way as to work correctly no
matter how the actual argument may be mapped onto abstract processors.

\subsubsection{Examples}

Here is a straightforward example of the use of \texttt{INHERIT}:

                                            \CODE

      REAL DOUGH(100)
!HPF$ DISTRIBUTE DOUGH(BLOCK(10))
      CALL PROBATE( DOUGH(7:23:2) )
      ...
      SUBROUTINE PROBATE(BREAD)
      REAL BREAD(9)
!HPF$ INHERIT BREAD
                                             \EDOC

The inherited template of \texttt{BREAD} has shape [100]; element 
\texttt{BREAD(I)} is aligned with element 5 + 2*I of the inherited
template, and that template has a \texttt{BLOCK(10)} distribution.


More complicated examples can easily be constructed.  It is important
to bear in mind that the inherited template may have a different rank
than the rank of the dummy, and it may even have a different rank than
the rank of the actual.  For instance, one might have a program
containing the following:

                                                \CODE
      REAL A(100,100)
!HPF$ TEMPLATE T(100,100,100)
!HPF$ DISTRIBUTE T(BLOCK,CYCLIC,*)
!HPF$ ALIGN A(I,J) with T(J,3,I)
      CALL SUBR(A(:,7))
      ...
      SUBROUTINE SUBR(D)
      REAL D(100)
!HPF$ INHERIT D
                                                 \EDOC

In this case, the dummy \texttt{D} has rank 1.  It corresponds to a
1-dimensional section of a 2-dimensional actual \texttt{A} which in
turn is aligned with a 2-dimensional section of a 3-dimensional
template \texttt{T}.  The ``visible'' dimension of the dummy is
distributed \texttt{*}, although if the call statement had been

                                                \CODE
      CALL SUBR(A(7,:))
                                                 \EDOC

\noindent
for instance, the ``visible'' dimension of the dummy would be
distributed \texttt{BLOCK}.


\subsection{ALIGN Directives}

The presence or absence of an asterisk at the start of an
\textit{align-spec} has the same meaning as in a
\textit{dist-format-clause}: it specifies whether the \texttt{ALIGN}
directive is descriptive or prescriptive, respectively.

If an \textit{align-spec} that does not begin with \texttt{*} is
applied to a dummy argument, the meaning is that the dummy argument
will be forced to have the specified alignment on entry to the
subprogram.  This may require either the caller or the subprogram to
temporarily remap the data of the actual argument or a copy thereof.

Note that a dummy argument may also be used as an \textit{align-target}.
                                                                        \CODE
      SUBROUTINE NICHOLAS(TSAR,CZAR)
      REAL, DIMENSION(1918) :: TSAR,CZAR
!HPF$ INHERIT :: TSAR
!HPF$ ALIGN WITH TSAR :: CZAR
                                                                        \EDOC

In this example the first dummy argument, \texttt{TSAR}, remains
aligned with the corresponding actual argument, while the second dummy
argument, \texttt{CZAR}, is forced to be aligned with the first dummy
argument.  If the two actual arguments are already aligned, no
remapping of the data will be required at run time.  If they are not,
some remapping will take place.

If the \textit{align-spec} begins with ``\texttt{*}'', then the
\textit{alignee} must be a dummy argument.  The ``\texttt{*}''
indicates that the \texttt{ALIGN} directive constitutes a guarantee on
the part of the programmer that, on entry to the subprogram, the
indicated alignment will already be satisfied by the dummy argument,
without any action to remap it required (on the part of the
subprogram) at run time.  For example:

                                                                        \CODE
      SUBROUTINE GRUNGE(PLUNGE,SPONGE)
      REAL PLUNGE(1000),SPONGE(1000)
!HPF$ INHERIT SPONGE
!HPF$ ALIGN PLUNGE WITH *SPONGE
                                                                        \EDOC

This asserts that, for every \texttt{J} in the range \texttt{1:1000},
on entry to subroutine \texttt{GRUNGE}, the directives in the program
have specified that \texttt{PLUNGE(J)} is currently mapped to the same
abstract processor as \texttt{SPONGE(J)}.

The intent is that if the language processor has in fact honored the
directives, then no interprocessor communication on the part of the
subprogram will be required to achieve the specified alignment.  As
usual, if an implementation performs all remapping in the caller, a
prescriptive form of the \texttt{ALIGN} directive would mean exactly
the same thing.

It is not permitted to say simply ``\texttt{ALIGN WITH *}''; an
\textit{align-target} must follow the asterisk.  (The proper way to
say ``accept any alignment'' is \texttt{INHERIT}.)

If a dummy argument has no explicit \texttt{ALIGN} or
\texttt{DISTRIBUTE} attribute, then the compiler provides an implicit
alignment and distribution specification, one that could have been
described explicitly without any ``assertion asterisks''.

\subsubsection{Example}

Without using \texttt{INHERIT}, explicit alignment of a dummy argument
may be necessary to insure that no remapping takes place at the
subroutine boundary.  Here is an example:

                                                                       \CODE
      LOGICAL FRUG(128)
!HPF$ PROCESSORS DANCE_FLOOR(16)
!HPF$ DISTRIBUTE (BLOCK) ONTO DANCE_FLOOR::FRUG
      CALL TERPSICHORE(FRUG(1:40:3))
                                                                        \EDOC

The array section \texttt{FRUG(1:40:3)} is mapped onto abstract
processors in the following manner:
\begin{center}
\setlength{\unitlength}{0.01in}
\begin{picture}(560,225)(0,0)
\put(0,200){\makebox(35,25){\small\rm 1}}
\put(35,200){\makebox(35,25){\small\rm 2}}
\put(70,200){\makebox(35,25){\small\rm 3}}
\put(105,200){\makebox(35,25){\small\rm 4}}
\put(140,200){\makebox(35,25){\small\rm 5}}
\put(175,200){\makebox(35,25){\small\rm 6}}
\put(210,200){\makebox(35,25){\small\rm 7}}
\put(245,200){\makebox(35,25){\small\rm 8}}
\put(280,200){\makebox(35,25){\small\rm 9}}
\put(315,200){\makebox(35,25){\small\rm 10}}
\put(350,200){\makebox(35,25){\small\rm 11}}
\put(385,200){\makebox(35,25){\small\rm 12}}
\put(420,200){\makebox(35,25){\small\rm 13}}
\put(455,200){\makebox(35,25){\small\rm 14}}
\put(490,200){\makebox(35,25){\small\rm 15}}
\put(525,200){\makebox(35,25){\small\rm 16}}
\thinlines
\multiput(0,25)(0,25){7}{\line(1,0){560}}
\thicklines
\multiput(0,0)(0,200){2}{\line(1,0){560}}
\multiput(0,0)(35,0){17}{\line(0,1){200}}
\put(0,175){\makebox(35,25){\tt 1}}
\put(0,100){\makebox(35,25){\tt 4}}
\put(0,25){\makebox(35,25){\tt 7}}
\put(35,150){\makebox(35,25){\tt 10}}
\put(35,75){\makebox(35,25){\tt 13}}
\put(35,0){\makebox(35,25){\tt 16}}
\put(70,125){\makebox(35,25){\tt 19}}
\put(70,50){\makebox(35,25){\tt 22}}
\put(105,175){\makebox(35,25){\tt 25}}
\put(105,100){\makebox(35,25){\tt 28}}
\put(105,25){\makebox(35,25){\tt 31}}
\put(140,150){\makebox(35,25){\tt 34}}
\put(140,75){\makebox(35,25){\tt 37}}
\put(140,0){\makebox(35,25){\tt 40}}
\end{picture}
\end{center}

Suppose first that the interface to the subroutine
\texttt{TERPSICHORE} looks like this:

                                                                        \CODE
      SUBROUTINE TERPSICHORE(FOXTROT)
      LOGICAL FOXTROT(:)
!HPF$ INHERIT FOXTROT
                                                                        \EDOC
The template of \texttt{FOXTROT} is a copy of the 128 element
template of the whole array \texttt{TWIST}.  The template is mapped like this:

\begin{center}
\setlength{\unitlength}{0.01in}
\begin{picture}(560,225)(0,0)
\put(0,200){\makebox(35,25){\small\rm 1}}
\put(35,200){\makebox(35,25){\small\rm 2}}
\put(70,200){\makebox(35,25){\small\rm 3}}
\put(105,200){\makebox(35,25){\small\rm 4}}
\put(140,200){\makebox(35,25){\small\rm 5}}
\put(175,200){\makebox(35,25){\small\rm 6}}
\put(210,200){\makebox(35,25){\small\rm 7}}
\put(245,200){\makebox(35,25){\small\rm 8}}
\put(280,200){\makebox(35,25){\small\rm 9}}
\put(315,200){\makebox(35,25){\small\rm 10}}
\put(350,200){\makebox(35,25){\small\rm 11}}
\put(385,200){\makebox(35,25){\small\rm 12}}
\put(420,200){\makebox(35,25){\small\rm 13}}
\put(455,200){\makebox(35,25){\small\rm 14}}
\put(490,200){\makebox(35,25){\small\rm 15}}
\put(525,200){\makebox(35,25){\small\rm 16}}
\thinlines
\multiput(0,25)(0,25){7}{\line(1,0){560}}
\thicklines
\multiput(0,0)(0,200){2}{\line(1,0){560}}
\multiput(0,0)(35,0){17}{\line(0,1){200}}
\put(0,175){\makebox(35,25){\tt 1}}
\put(0,150){\makebox(35,25){\tt 2}}
\put(0,125){\makebox(35,25){\tt 3}}
\put(0,100){\makebox(35,25){\tt 4}}
\put(0,75){\makebox(35,25){\tt 5}}
\put(0,50){\makebox(35,25){\tt 6}}
\put(0,25){\makebox(35,25){\tt 7}}
\put(0,0){\makebox(35,25){\tt 8}}
\put(35,175){\makebox(35,25){\tt 9}}
\put(35,150){\makebox(35,25){\tt 10}}
\put(35,125){\makebox(35,25){\tt 11}}
\put(35,100){\makebox(35,25){\tt 12}}
\put(35,75){\makebox(35,25){\tt 13}}
\put(35,50){\makebox(35,25){\tt 14}}
\put(35,25){\makebox(35,25){\tt 15}}
\put(35,0){\makebox(35,25){\tt 16}}
\put(70,175){\makebox(35,25){\tt 17}}
\put(70,150){\makebox(35,25){\tt 18}}
\put(70,125){\makebox(35,25){\tt 19}}
\put(70,100){\makebox(35,25){\tt 20}}
\put(70,75){\makebox(35,25){\tt 21}}
\put(70,50){\makebox(35,25){\tt 22}}
\put(70,25){\makebox(35,25){\tt 23}}
\put(70,0){\makebox(35,25){\tt 24}}
\put(105,175){\makebox(35,25){\tt 25}}
\put(105,150){\makebox(35,25){\tt 26}}
\put(105,125){\makebox(35,25){\tt 27}}
\put(105,100){\makebox(35,25){\tt 28}}
\put(105,75){\makebox(35,25){\tt 29}}
\put(105,50){\makebox(35,25){\tt 30}}
\put(105,25){\makebox(35,25){\tt 31}}
\put(105,0){\makebox(35,25){\tt 32}}
\put(140,175){\makebox(35,25){\tt 33}}
\put(140,150){\makebox(35,25){\tt 34}}
\put(140,125){\makebox(35,25){\tt 35}}
\put(140,100){\makebox(35,25){\tt 36}}
\put(140,75){\makebox(35,25){\tt 37}}
\put(140,50){\makebox(35,25){\tt 38}}
\put(140,25){\makebox(35,25){\tt 39}}
\put(140,0){\makebox(35,25){\tt 40}}
\put(175,175){\makebox(35,25){\tt 41}}
\put(175,150){\makebox(35,25){\tt 42}}
\put(175,125){\makebox(35,25){\tt 43}}
\put(175,100){\makebox(35,25){\tt 44}}
\put(175,75){\makebox(35,25){\tt 45}}
\put(175,50){\makebox(35,25){\tt 46}}
\put(175,25){\makebox(35,25){\tt 47}}
\put(175,0){\makebox(35,25){\tt 48}}
\put(210,175){\makebox(35,25){\tt 49}}
\put(210,150){\makebox(35,25){\tt 50}}
\put(210,125){\makebox(35,25){\tt 51}}
\put(210,100){\makebox(35,25){\tt 52}}
\put(210,75){\makebox(35,25){\tt 53}}
\put(210,50){\makebox(35,25){\tt 54}}
\put(210,25){\makebox(35,25){\tt 55}}
\put(210,0){\makebox(35,25){\tt 56}}
\put(245,175){\makebox(35,25){\tt 57}}
\put(245,150){\makebox(35,25){\tt 58}}
\put(245,125){\makebox(35,25){\tt 59}}
\put(245,100){\makebox(35,25){\tt 60}}
\put(245,75){\makebox(35,25){\tt 61}}
\put(245,50){\makebox(35,25){\tt 62}}
\put(245,25){\makebox(35,25){\tt 63}}
\put(245,0){\makebox(35,25){\tt 64}}
\put(280,175){\makebox(35,25){\tt 65}}
\put(280,150){\makebox(35,25){\tt 66}}
\put(280,125){\makebox(35,25){\tt 67}}
\put(280,100){\makebox(35,25){\tt 68}}
\put(280,75){\makebox(35,25){\tt 69}}
\put(280,50){\makebox(35,25){\tt 70}}
\put(280,25){\makebox(35,25){\tt 71}}
\put(280,0){\makebox(35,25){\tt 72}}
\put(315,175){\makebox(35,25){\tt 73}}
\put(315,150){\makebox(35,25){\tt 74}}
\put(315,125){\makebox(35,25){\tt 75}}
\put(315,100){\makebox(35,25){\tt 76}}
\put(315,75){\makebox(35,25){\tt 77}}
\put(315,50){\makebox(35,25){\tt 78}}
\put(315,25){\makebox(35,25){\tt 79}}
\put(315,0){\makebox(35,25){\tt 80}}
\put(350,175){\makebox(35,25){\tt 81}}
\put(350,150){\makebox(35,25){\tt 82}}
\put(350,125){\makebox(35,25){\tt 83}}
\put(350,100){\makebox(35,25){\tt 84}}
\put(350,75){\makebox(35,25){\tt 85}}
\put(350,50){\makebox(35,25){\tt 86}}
\put(350,25){\makebox(35,25){\tt 87}}
\put(350,0){\makebox(35,25){\tt 88}}
\put(385,175){\makebox(35,25){\tt 89}}
\put(385,150){\makebox(35,25){\tt 90}}
\put(385,125){\makebox(35,25){\tt 91}}
\put(385,100){\makebox(35,25){\tt 92}}
\put(385,75){\makebox(35,25){\tt 93}}
\put(385,50){\makebox(35,25){\tt 94}}
\put(385,25){\makebox(35,25){\tt 95}}
\put(385,0){\makebox(35,25){\tt 96}}
\put(420,175){\makebox(35,25){\tt 97}}
\put(420,150){\makebox(35,25){\tt 98}}
\put(420,125){\makebox(35,25){\tt 99}}
\put(420,100){\makebox(35,25){\tt 100}}
\put(420,75){\makebox(35,25){\tt 101}}
\put(420,50){\makebox(35,25){\tt 102}}
\put(420,25){\makebox(35,25){\tt 103}}
\put(420,0){\makebox(35,25){\tt 104}}
\put(455,175){\makebox(35,25){\tt 105}}
\put(455,150){\makebox(35,25){\tt 106}}
\put(455,125){\makebox(35,25){\tt 107}}
\put(455,100){\makebox(35,25){\tt 108}}
\put(455,75){\makebox(35,25){\tt 109}}
\put(455,50){\makebox(35,25){\tt 110}}
\put(455,25){\makebox(35,25){\tt 111}}
\put(455,0){\makebox(35,25){\tt 112}}
\put(490,175){\makebox(35,25){\tt 113}}
\put(490,150){\makebox(35,25){\tt 114}}
\put(490,125){\makebox(35,25){\tt 115}}
\put(490,100){\makebox(35,25){\tt 116}}
\put(490,75){\makebox(35,25){\tt 117}}
\put(490,50){\makebox(35,25){\tt 118}}
\put(490,25){\makebox(35,25){\tt 119}}
\put(490,0){\makebox(35,25){\tt 120}}
\put(525,175){\makebox(35,25){\tt 121}}
\put(525,150){\makebox(35,25){\tt 122}}
\put(525,125){\makebox(35,25){\tt 123}}
\put(525,100){\makebox(35,25){\tt 124}}
\put(525,75){\makebox(35,25){\tt 125}}
\put(525,50){\makebox(35,25){\tt 126}}
\put(525,25){\makebox(35,25){\tt 127}}
\put(525,0){\makebox(35,25){\tt 128}}
\end{picture}
\end{center}

\noindent
\texttt{FOXTROT(I)} is aligned with element 3*I-2 of the template.

Suppose on the other hand that the interface to \texttt{TERPSICHORE} looks
like this:

                                                                        \CODE
      SUBROUTINE TERPSICHORE(FOXTROT)
      LOGICAL FOXTROT(:)
!HPF$ DISTRIBUTE FOXTROT(BLOCK)
                                                                        \EDOC


In this case, the template of \texttt{FOXTROT} is its natural
template; it has the same size 14 as \texttt{FOXTROT} itself.  The
actual argument, \texttt{FRUG(1:40:3)} is mapped to the 16 processors
in this manner:

\begin{center}
\begin{tabular}{cc}
Abstract  &  Elements \\
processor & of FRUG \\
1 & 1, 2, 3 \\
2 & 4, 5, 6 \\
3 & 7, 8 \\
4 & 9, 10, 11 \\
5 & 12, 13, 14 \\
6--16   &  none
\end{tabular}
\end{center}

That is, the original positions (in the template of the actual
argument) of the elements of the dummy are as follows:

\begin{center}
\setlength{\unitlength}{0.01in}
\begin{picture}(560,225)(0,0)
\put(0,200){\makebox(35,25){\small\rm 1}}
\put(35,200){\makebox(35,25){\small\rm 2}}
\put(70,200){\makebox(35,25){\small\rm 3}}
\put(105,200){\makebox(35,25){\small\rm 4}}
\put(140,200){\makebox(35,25){\small\rm 5}}
\put(175,200){\makebox(35,25){\small\rm 6}}
\put(210,200){\makebox(35,25){\small\rm 7}}
\put(245,200){\makebox(35,25){\small\rm 8}}
\put(280,200){\makebox(35,25){\small\rm 9}}
\put(315,200){\makebox(35,25){\small\rm 10}}
\put(350,200){\makebox(35,25){\small\rm 11}}
\put(385,200){\makebox(35,25){\small\rm 12}}
\put(420,200){\makebox(35,25){\small\rm 13}}
\put(455,200){\makebox(35,25){\small\rm 14}}
\put(490,200){\makebox(35,25){\small\rm 15}}
\put(525,200){\makebox(35,25){\small\rm 16}}
\thinlines
\multiput(0,25)(0,25){7}{\line(1,0){560}}
\thicklines
\multiput(0,0)(0,200){2}{\line(1,0){560}}
\multiput(0,0)(35,0){17}{\line(0,1){200}}
\put(0,175){\makebox(35,25){\tt 1}}
\put(0,100){\makebox(35,25){\tt 2}}
\put(0,25){\makebox(35,25){\tt 3}}
\put(35,150){\makebox(35,25){\tt 4}}
\put(35,75){\makebox(35,25){\tt 5}}
\put(35,0){\makebox(35,25){\tt 6}}
\put(70,125){\makebox(35,25){\tt 7}}
\put(70,50){\makebox(35,25){\tt 8}}
\put(105,175){\makebox(35,25){\tt 9}}
\put(105,100){\makebox(35,25){\tt 10}}
\put(105,25){\makebox(35,25){\tt 11}}
\put(140,150){\makebox(35,25){\tt 12}}
\put(140,75){\makebox(35,25){\tt 13}}
\put(140,0){\makebox(35,25){\tt 14}}
\end{picture}
\end{center}

This layout (3 elements on the first processor, 3 on the second, 2 on
the third, 3 on the fourth, \dots) cannot properly be described as a
\texttt{BLOCK} distribution.  Therefore, remapping will take place at
the call.

Remapping can be avoided without using \texttt{INHERIT} by explicitly
aligning the dummy to a declared template of size 128 distributed
\texttt{BLOCK}:

                                                                        \CODE
      SUBROUTINE TERPSICHORE(FOXTROT)
      LOGICAL FOXTROT(:)
!HPF$ PROCESSORS DANCE_FLOOR(16)
!HPF$ TEMPLATE, DISTRIBUTE(BLOCK) ONTO DANCE_FLOOR::GURF(128)
!HPF$ ALIGN FOXTROT(J) WITH GURF(3*J-2)
                                                                        \EDOC

\begin{users}
  The advantage of this technique is that, where it can be used, it
  gives the compiler more information; this information can often be
  used to generate more efficient code.
\end{users}

\section{Explicit Interfaces}
\label{mapsub:ExplicitInterfaces}

An explicit interface is required \emph{except} when all four of the
following conditions hold:

\begin{enumerate}

\item  Fortran does not require one, \emph{and}
  
\item No dummy argument is passed transcriptively or with the
  \texttt{INHERIT} attribute, \emph{and}

\item For each pair of corresponding actual and dummy arguments, either:

  \begin{enumerate}

  \item They are both implicitly mapped, or

  \item They are both explicitly mapped and the conditions in
    Section~\ref{mapsub:NoExplicitInterface} are satisfied.

  \end{enumerate}

  \emph{and}

\item For each pair of corresponding actual and dummy arguments, either:

  \begin{enumerate}

  \item Both are sequential, or

  \item Both are nonsequential.

  \end{enumerate}

\end{enumerate}

\begin{rationale}
  This has the following consequences:

  \begin{itemize}

  \item A plain Fortran program (i.e., with no HPF directives) will
    continue to be legal without the need to add additional interfaces.
    This is insured by items 1, 2, 3a, and 4a.
  
  \item If remapping is necessary, this fact will be visible to the
    caller.  Thus the implementation may choose to have all remapping
    performed by the caller.

  \end{itemize}
\end{rationale}

\begin{users}
  This requirement pushes the user strongly in the direction of always
  providing explicit interfaces.  This is a good thing---explicit
  interfaces allow many errors to be caught at compile-time and greatly
  speed up the process of robust software development.

  Note, that an explicit interface can be provided in three ways:

  \begin{enumerate}

  \item Module procedures have an explicit interface.

  \item Contained subprograms have an explicit interface.

  \item An explicit interface may be provided by an interface block.

  \end{enumerate}

  In addition, an intrinsic procedure always has an explicit interface
  by definition.

  The idiomatic Fortran way of programming makes extensive use of
  modules; every subroutine, for instance, can be in a module.  This
  provides explicit interfaces automatically, with no extra effort on
  the part of the programmer.  It should very seldom be necessary to
  write an interface block.
\end{users}


\subsection{Explicit Mappings Without an Explicit Interface}
\label{mapsub:NoExplicitInterface}

When there is no explicit interface, the actual and dummy arguments
may still be explicitly mapped (but not transcriptively or with the
\texttt{INHERIT} attribute), as long as the conditions in this section
are satisfied.

\begin{users}
  These conditions are complex.  The important thing to realize is
  that you don't have to read any of this if you have an explicit
  interface.  So if there is any doubt in your mind, just make sure
  you have an explicit interface.
\end{users}

\begin{enumerate}
  
\item The actual argument must be a named object.  (So for instance,
  the actual argument cannot be an array section.)
  
\item The shapes of the ultimate align targets of the dummy and the
  actual must be the same.

\item Either

  \begin{enumerate}
  \item the ultimate align targets of the dummy and actual must not
    have been explicitly distributed, or
    
  \item the \texttt{DISTRIBUTE} directives specified for both ultimate
    align targets must

    \begin{enumerate}
    \item have a \textit{dist-onto-clause} specifying processor
      arrangements with the same shape; and
      
    \item specify a \textit{dist-format-clause} with the same
      \textit{dist-format}s in corresponding positions, except that a
      \textit{dist-format} of \texttt{BLOCK} is regarded as the same
      as a \textit{dist-format} of \texttt{BLOCK(\(n\))} if the the
      actual blocking size of the \texttt{BLOCK} distribution has the
      same value as \(n\); and the same for \texttt{CYCLIC} and
      \texttt{CYCLIC(\(n\))}.
    \end{enumerate}
  \end{enumerate}

\item Each dimension of the actual and dummy must correspond to the same
  dimension of their respective ultimate align targets, and
  corresponding elements of the actual and dummy must be aligned with
  the same corresponding elements of their respective ultimate align
  targets.
\end{enumerate}


\section{Restrictions on Pointers and Targets}
\label{mapsub:pointers}

If, on invocation of a procedure P: (a)~a dummy argument has the
\texttt{TARGET} attribute, and (b)~the corresponding actual argument
has the \texttt{TARGET} attribute and is not an array section with a
vector subscript (and therefore is an object A or a section of an
array A), then the program is not HPF-conforming unless:
\begin{enumerate}
\item No remapping of the actual argument occurs during the call; or
\item the remainder of program execution would be unaffected if
  \begin{enumerate}
  \item each pointer associated with any portion of the dummy
    argument or with any portion of A during execution of P were to
    acquire undefined pointer association status on exit from P; and
  \item each pointer associated with any portion of A before the
    call were to acquire undefined pointer association status on
    entry to P and, if not reassigned during execution of P, were to
    be restored on exit to the pointer association status it had
    before entry.
  \end{enumerate}
\end{enumerate}

Note that if a dummy argument has the \texttt{TARGET} attribute and no
explicit mapping attributes, then the \texttt{INHERIT} attribute is
implicitly assumed (see section~\ref{INHERIT-SECTION}); therefore no
remapping occurs for such a dummy argument and there is no problem.

\begin{rationale}
  These restrictions are made in order to support the following part
  of the Fortran standard (in Section 12.4.1.1 of that document) in
  the face of implicit remapping across the subprogram interface:
\begin{quote}
If the dummy argument does not have the \texttt{TARGET} or \texttt{POINTER}
attribute, any pointers associated with the actual argument do not become
associated with the corresponding dummy argument on invocation of the procedure.

If the dummy argument has the \texttt{TARGET} attribute and the
corresponding actual argument has the \texttt{TARGET} attribute but is
not an array section with a vector subscript:
\begin{enumerate}
\item Any pointers associated with the actual argument become
  associated with the corresponding dummy argument on invocation of
  the procedure.
  
\item When execution of the procedure completes, any pointers
  associated with the dummy argument remain associated with the actual
  argument.
\end{enumerate}

If the dummy argument has the \texttt{TARGET} attribute and the
corresponding actual argument does not have the \texttt{TARGET}
attribute or is an array section with a vector subscript, any pointers
associated with the dummy argument become undefined when execution of
the procedure completes.
\end{quote}
\end{rationale}


\section{Argument Passing and Sequence Association}

For actual arguments in a procedure call, Fortran allows an array
element (scalar) to be associated with a dummy argument that is an
array.  It furthermore allows the shape of a dummy argument to differ
from the shape of the corresponding actual array argument, in effect
reshaping the actual argument via the subroutine call.  Storage
sequence properties of Fortran are used to identify the values of the
dummy argument.  This feature, carried over from FORTRAN 77, has been
widely used to pass starting addresses of subarrays, rows or columns
of a larger array, to procedures.  For HPF arrays that are potentially
mapped across processors, this feature is not fully supported.


\subsection{Sequence Association Rules}

\begin{enumerate}
  
\item When an array element or the name of an assumed-size array is
  used as an actual argument, the associated dummy argument must be a
  scalar or specified to be a sequential array.
  
  An array-element designator of a nonsequential array must not be
  associated with a dummy array argument.
  
\item When an actual argument is an array or array section and the
  corresponding dummy argument differs from the actual argument in
  shape, then the dummy argument must be declared sequential and the
  actual array argument must be sequential.
  
\item An object of type character (scalar or array) is nonsequential
  if it conforms to the requirements of Definition~\ref{seq-var} of
  Section~\ref{sequence-defs}.  If the length of an explicit-length
  character dummy argument differs from the length of the actual
  argument, then both the actual and dummy arguments must be
  sequential.

  
\item Without an explicit interface, a sequential actual may not be
  associated with a nonsequential dummy and a nonsequential actual may
  not be associated with a sequential dummy.  (This item merely
  repeats part of Section~\ref{mapsub:ExplicitInterfaces}


\end{enumerate}


\subsection{Discussion of Sequence Association}

When the shape of the dummy array argument and its associated actual
array argument differ, the actual argument must not be an expression.
There is no HPF mechanism for declaring that the value of an
array-valued expression is sequential.  In order to associate such an
expression as an actual argument with a dummy argument of different
rank, the actual argument must first be assigned to a named array
variable that is forced to be sequential according to
Definition~\ref{seq-var} of Section~\ref{sequence-defs}.

\subsection{Examples of Sequence Association}

Given the following subroutine fragment:
                                                                \CODE
      SUBROUTINE HOME (X)
      DIMENSION X (20,10)
                                                                \EDOC
By rule 1
                                                                \CODE
      CALL HOME (ET (2,1))
                                                                \EDOC
is legal only if \texttt{X} is declared sequential in \texttt{HOME}
and \texttt{ET} is sequential in the calling routine.

Likewise, by rule 2 and 4
                                                                \CODE
      CALL HOME (ET)
                                                                \EDOC
requires either that \texttt{ET} and \texttt{X} are both sequential arrays or 
that \texttt{ET} and \texttt{X} have the same shape and have the same
sequence attribute.


Rule 3 addresses a special consideration for  objects of type 
character. Change of the length of character objects across 
a call, as in

                                                                \CODE
      CHARACTER (LEN=44) one_long_word
      one_long_word = 'Chargoggagoggmanchaugagoggchaubunagungamaugg'
      CALL webster(one_long_word)

      SUBROUTINE webster(short_dictionary)
      CHARACTER (LEN=4) short_dictionary (11)
          !Note that short_dictionary(3) is 'agog', for example
                                                                \EDOC

\noindent
is conceptually legal in FORTRAN 77 and Fortran 95. In HPF, both the
actual argument and dummy argument must be sequential.
(Chargoggagoggmanchaugagoggchaubunagungamaugg is the original Nipmuc
name for what is now called Lake Webster in Massachusetts.)

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Hello,

     Here's the latest draft of the Interoperability with C stuff.  I wasn't
sure how much of the MAP_TO would be described here and how much would be
described in the general section on extrinsic interfaces; I kept the syntax of
MAP_TO, but dropped the syntax for EXTERNAL_NAME.  There are still many
references to EXTRINSIC(C), which is no longer the correct name.

     I've also had a request from Michael Hennecke to split the sub-specifiers
of MAP_TO into separate specifiers - so rather than specifying something like:

        INTEGER, MAP_TO(TYPE='int', PASSBY='ref', LAYOUT='c_array') :: I(10)

we'd have

        INTEGER, MAP_TO('int'), PASSBY('ref'), LAYOUT('c_array') :: I(10)

but that's not been incorporated.  I'll describe it at the next meeting.

     Please check the notes to reviewers for some of the unresolved issues.

Thanks,

Henry

%%% Start temporary stuff

\newenvironment{reviewers}{\begin{list}{}{}\item[]{\it Note
        to reviewers.}
}{{\rm ({\it End of note to reviewers.})} \end{list}}

%%% End temporary stuff

% interop.tex

% Initial Version of June 21, 1996
% Andy Meltzer and Henry Zongaro
% Version 0.1 - July 11, 1996
% Version 0.2 - August 2, 1996

\chapter{Approved Extension for HPF Interoperability with C}
\label{ch-interop}

{\em
Comments on this chapter should be directed to Henry Zongaro
({\tt zongaro@vnet.ibm.com}), Andy Meltzer ({\tt meltzer@cray.com}) and
{\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Interoperability}'' as the {\tt Subject:}
line.
\par
}

A common problem faced by Fortran users is the need to call procedures
written in other languages, particularly those writen in C or which have
interfaces that can be described by C prototypes.  Although many Fortran
implementations provide methods which solve this problem, these solutions are
rarely portable.

This section defines a method of specifying interfaces to procedures defined
in C that removes most of the common obstacles to interoperability, while
retaining portability.

\section{Specification of Interfaces to Procedures Defined in C}

\begin{reviewers}
This section needs to be harmonized with the recent changes to the
{\tt EXTRINSIC} attribute.
\end{reviewers}
If a user wishes to specify that a procedure is defined by a C procedure,
this is specified with an {\it extrinsic-kind-keyword} of {\tt C}, as specified
in Section ??.

% \BNF
% function-stuff    \IS  ( [ dummy-arg-name-list ] ) [ postfix ]
%
% subroutine-stuff  \IS  [ ( [ dummy-arg-list ] ) ] [ postfix ]
%
% postfix           \IS  postfix-spec [ postfix-spec ] ...
%
% postfix-spec      \IS  RESULT ( result-name )
%                   \OR  EXTERNAL_NAME ( char-literal-constant )
% \FNB

\begin{constraints}

% \item  A {\it postfix} shall contain no more than one of each type of
%       {\it postfix-spec}.
%
% \item  {\tt RESULT} shall not be specified as part of a {\it subroutine-stmt}.
%
% \item  {\tt EXTERNAL_NAME} shall only be specified as part of a
%        {\it subroutine-stmt} or {\it function-stmt} for which a
%        {\it prefix-spec} of {\tt EXTRINSIC(C)} has been specified.

\item  A function for which a {\it prefix-spec} of {\tt EXTRINSIC(C)} has
       been specified shall have a scalar result of type integer, real or
       double precision real.

\item  A dummy argument of a procedure for which a {\it prefix-spec} of
       {\tt EXTRINSIC(C)} has been specified shall not be an assumed-shape
       array, shall not have the {\tt POINTER} attribute, shall not have the
       {\tt TARGET} attribute, nor shall it have a subobject which has the
       {\tt POINTER} attribute.

\item  The bounds of a dummy argument of a procedure for which a
       {\it prefix-spec} of {\tt EXTRINSIC(C)} has been specified shall not
       be specified by specification expressions which are not constant
       specification expressions, nor shall the character length parameter
       of a dummy argument of such a procedure be specified by a specification
       expression which is not a constant specification expression.

\item  A {\it dummy-arg-list} of a subroutine which has an
       {\it extrinsic-kind-keyword} of {\tt C} shall not have a {\it dummy-arg}
       which is {\tt *} or a dummy procedure.
\end{constraints}

The value of the {\it char-literal-constant} in the {\tt EXTERNAL_NAME}
specifier gives the name of the procedure as defined in C.  This value need
not be the same as the procedure name specified by the {\it function-stmt}
or {\it subroutine-stmt}.  If {\tt EXTERNAL_NAME} is not specified, it is
as if it was specified with a value which is the same as the procedure name
in lower case letters.

% \begin{reviewers}
% Should we force user to specify {\tt EXTERNAL_NAME}?  If not, should the
% folding be to lower case or upper?  Although lower case folding is common in
% UNIX environments, is it common elsewhere?
% \end{reviewers}

% Syntax rule H6?? is rewritten here:
% \BNF
% extrinsic-kind-keyword  \IS  HPF
%                         \OR  HPF_LOCAL
%                         \OR  HPF_SERIAL
%                         \OR  C
% \FNB

%\begin{constraints}

% \item  An {\it extrinsic-kind-keyword} of {\tt C} shall only be specified
%        as part of the {\it function-stmt} or {\it subroutine-stmt} of a
%        procedure that is declared to be a procedure by an interface body.
%
%\end{constraints}

The {\tt EXTRINSIC(C)} {\it prefix-spec} helps a compiler identify a procedure
that is defined in C, so that it can take appropriate steps to ensure that
the procedure is invoked in the manner required by the C compiler.

\begin{implementors}
A vendor may feel compelled to provide support for more than one C compiler,
if different C compilers available for a system provide different procedure
calling conventions or different data type sizes.  For instance, a vendor's
compiler may provide support for an {\tt EXTRINSIC(GNU_C)} {\it prefix-spec},
or it may provide support through the use of compiler switches.
\end{implementors}

\section{Specification of Data Type Mappings}

The {\tt MAPTO} attribute is the principle new feature which facilitates
referencing procedures defined in C from within Fortran programs.  It allows
the user to specify conversions required to associate the actual arguments
specified on the procedure reference with the formal arguments defined by
the referenced procedure.  The attribute has several optional specifiers.  The
TYPE= specifier indicates the type of the C data to which the HPF data shall
be converted by the compiler; the PASSBY= specifier indicates whether a C
pointer to the dummy argument needs to be passed; the LAYOUT= specifier
indicates for an array whether the array element order needs to be changed from
Fortran's array element ordering to C's.

\BNF
attr-spec  \IS  MAPTO ( [ TYPE= ] mapto-type-spec
                        [ , [ PASSBY= ] passby-spec ]
                        [ , [ LAYOUT= ] layout-spec ] )

mapto-type-spec \IS  default-char-literal-constant

% mapto-type-spec \IS  INT
%           \OR  LONG
%           \OR  SHORT
%           \OR  CHAR
%           \OR  FLOAT
%           \OR  DOUBLE
%           \OR  LONG_DOUBLE
%           \OR  CHAR_PTR
%           \OR  struct-mapto

% struct-mapto  \IS  ( mapto-type-spec-list )

layout-spec   \IS  default-char-literal-constant

passby-spec \IS  default-char-literal-constant
\FNB

\begin{constraints}

\item  The {\tt MAPTO} attribute shall only be specified for a dummy argument
       or function result variable of a function or subroutine which has an
       {\it extrinsic-kind-keyword} of {\tt C}.  In addition, the {\tt MAPTO}
       attribute shall be specified for all such dummy arguments and function
       result variables.

\item  If the {\tt MAPTO} attribute is specified for a variable, the
       {\it mapto-type-spec} specified shall be compatible with the type of the
       variable.

\item  The {\it layout-spec} specifier of the {\tt MAPTO} attribute shall only
       be specified for a dummy argument which is an array.

\item  A {\it layout-spec} shall not be specified for an assumed-size array.
\end{constraints}

If the compiler is capable of representing letters in both upper and lower
case, the value specified for a {\it mapto-type-spec}, {\it layout-spec}
or {\it passby-spec} is without regard to case.  Any blanks specified for a
{\it mapto-type-spec}, {\it layout-spec} or {\it passby-spec} shall be ignored
by the compiler for the purposes of determining its value.

\begin{reviewers}
I don't believe the following definition of {\tt C_VOID_POINTER} is going to
work.  This can get us to {\tt void *}, but what about {\tt int *},
{\tt float *}, etc. that might appear within {\tt struct} definitions?  Or
do we turn a blind eye and not support them?
\end{reviewers}

An implementation shall provide a module, {\tt ISO_C}, which shall define a
derived type, {\tt C_VOID_POINTER}.  The components of the {\tt C_VOID_POINTER}
type shall be private.

\begin{users}
The {\tt C_VOID_POINTER} type provides a method of using {\tt void *}
pointers in a program, but does not give the user any way of manipulating
such a pointer in the Fortran part of the program, since I/O cannot be
performed on an object with private components outside the module which defines
the type, neither can the components or structure constructor of such a
structure be used outside of the module which defines the type.
\end{users}

\begin{reviewers}
I will be the first to admit that the following on mapped to types is very
difficult to read.  Any suggestions for improvement will be happily
entertained.
\end{reviewers}

The values permitted for a {\it mapto-type-spec} are {\tt INT}, {\tt LONG},
{\tt SHORT}, {\tt CHAR}, {\tt FLOAT}, {\tt DOUBLE}, {\tt LONG_DOUBLE},
{\tt CHAR_PTR}, {\tt VOID_PTR}
or a comma-separated list, delimited by parentheses, of values
which are permitted for a {\it mapto-type-spec}.

A {\it mapto-type-spec} whose value is {\tt INT}, {\tt LONG}, {\tt SHORT}
or {\tt CHAR} is
compatible with the intrinsic type integer.  A {\it mapto-type-spec} whose
value is
{\tt FLOAT}, {\tt DOUBLE} or {\tt LONG_DOUBLE} is compatible with the intrinsic
type real.
A {\it mapto-type-spec} whose value is {\tt CHAR_PTR} is compatible with the
intrinsic type
character.  A {\it mapto-type-spec} whose value is {\tt VOID_PTR} is compatible
with the derived type {\tt C_VOID_POINTER} defined by the module {\tt ISO_C}.
A {\it mapto-type-spec} which is a parenthesised list of values is
compatible with a derived type if each value in the list
is compatible with the corresponding components of the
derived type.

The values permitted for a {\it passby-spec} are {\tt VAL}, {\tt REF},
{\tt RREF}, {\tt RRREF} or {\tt RRRREF}.  If the {\it passby-spec}
is not specified, the value {\tt VAL} is assumed.  If a {\it passby-spec} of
{\tt VAL} is specified, the dummy argument shall not have the
{\tt INTENT(OUT)} or {\tt INTENT(INOUT)} attribute specified.  If a value of
{\tt REF}, {\tt RREF}, {\tt RRREF} or {\tt RRRREF} is specified for the
{\it passby-spec}, an associated actual argument shall be a variable.

The value of the {\it mapto-type-spec} specified for a dummy argument in
the interface body of a procedure with the {\tt EXTRINSIC(C)}
{\it prefix-spec} shall be such that at
least one of the permitted mapped to types is the same as
the C data type of the corresponding formal argument in the C
definition of the procedure (or a type that is equivalent to one of the
permitted mapped to types).
The C data type of a function in the C
definition of a procedure shall be one of the permitted mapped to types
(or a type that is equivalent to the permitted mapped to types) specified
for the function result variable specified in the interface body of a
function with the {\tt EXTRINSIC(C)} {\it prefix-spec}.
  If a subroutine has
been specified with a {\it prefix-spec} of {\tt EXTRINSIC(C)}, the C definition
of the procedure shall be specified with a data type of {\tt void}.

\begin{reviewers}
I'm not sure how the C standard describes types that are "equivalent".  Anyone
know the correct terminology?
\end{reviewers}

The permitted mapped to types of a scalar variable of intrinsic type,
when the value specified for the {\tt PASSBY} keyword is {\tt VAL}:
\begin{itemize}
\item  is {\tt int} if a {\it mapto-type-spec} of {\tt INT} is specified for the
       variable;
\item  is {\tt long} if a {\it mapto-type-spec} of {\tt LONG} is specified
       for the variable;
\item  is {\tt short} if a {\it mapto-type-spec} of {\tt SHORT} is specified
       for the variable;
\item  is {\tt char} if a {\it mapto-type-spec} of {\tt CHAR} is specified
       for the variable;
\item  is {\tt float} if a {\it mapto-type-spec} of {\tt FLOAT} is specified
       for the variable;
\item  is {\tt double} if a {\it mapto-type-spec} of {\tt DOUBLE} is specified
       for the variable;
\item  is {\tt long double} if a {\it mapto-type-spec} of {\tt LONG_DOUBLE}
       is specified for the variable; or
\item  are {\tt char *} if a {\it mapto-type-spec} of {\tt CHAR_PTR} is
       specified for the variable.
\item  is {\tt void *} if a {\it mapto-type-spec} of {\tt VOID_PTR}
\end{itemize}

The permitted mapped to types of an array are the same as the permitted mapped
to types of a scalar variable of that type followed by a left bracket
({\tt [}),
followed by the extent of the corresponding dimension of the dummy argument,
following by a right bracket ({\tt ]}), for each dimension of the array.  If
no value is specified for the {\tt LAYOUT=} specifier, the corresponding
dimensions of the dummy argument are determined from right to left; if the
value C_ARRAY is specified for the {\tt LAYOUT=} specifier, the corresponding
dimensions of the dummy argument are determined from left to right.

The permitted mapped to types of a scalar variable of derived type are the
structures whose members are of one of the permitted mapped to types of the
components of the derived type.

The permitted mapped to types of a dummy argument, when the value specified
for the {\tt PASSBY} keyword is {\tt REF}, {\tt RREF}, {\tt RRREF} or
{\tt RRRREF}, are the same as the permitted mapped to types of such a dummy
argument when the {\tt PASSBY} keyword is {\tt VAL}, except that for {\tt REF}
the permitted mapped to types have a single {\tt *} (asterisk) appended,
for {\tt RREF} two asterisks are appended, for {\tt RRREF} three asterisks are
appended, and for {\tt RRRREF} four asterisks are appended.

\begin{reviewers}
There was some feeling at the May meeting that permitting {\tt RREF}
to help map to pointers to pointers wasn't really beneficial.  Mainly, it
was felt that people use things like {\tt int **p} when they want to return
(or modify) a pointer to a buffer area, and that there would be no way of
accessing something like that on the Fortran side via the {\tt RREF}.

Opinions?
\end{reviewers}

If there is a mismatch between the precision, representation method, range of
permitted values or storage sequence between the type of the dummy argument and
the permitted mapped to type of the dummy argument, the compiler shall ensure
that, for the duration of the reference to a procedure defined with an
{\it extrinsic-kind-keyword} of {\tt C}, the dummy argument is represented in
a manner that is compatible with the expectations of the C processor for an
object of the permitted mapped to type.  Upon return from the procedure, the
compiler shall ensure that the value of an actual argument which is a variable
is restored to the specified type and kind.

\begin{users}
This rule was created to ensure the portability of interoperability.  However,
it should be noted that for large objects, a significant overhead may be
incurred if there is a mismatch between the representation method used for
the data type versus the representation method used for the permitted mapped to
type.
\end{users}

\begin{users}
In some cases, this may cause the value of the actual argument to change
without the value being modified by the procedure referenced.  For example,

\CODE
      PROGRAM P
        INTERFACE
          EXTRINSIC(C) SUBROUTINE C_SUB(R)
            REAL(KIND(1.0D0)), MAPTO('FLOAT', 'REF') :: R
          END SUBROUTINE C_SUB
        END INTERFACE
        REAL(KIND(0.0D0))

        R = 1.0D0 + 1.0D-10
        PRINT *, R
        CALL C_SUB(R)
        PRINT *, R
      END PROGRAM P

      void c_sub(float *r)
      {
      }
\EDOC

Might print

\CODE
 1.00000000050000004
 1.00000000000000000
\EDOC

although the value of {\tt *r} is not modified in {\tt c_sub}.
\end{users}

If the range of permitted values of the type and mapped to type differ and
the value of the actual argument or some subobject of the actual argument is
not within the permitted range of the mapped to type, the value of the
associated dummy argument or subobject becomes undefined.  Conversely, if
the value of the dummy argument or some subobject of the dummy is not within
the permitted range of values of the associated dummy argument, and the
associated actual argument is a variable, the value of the associated actual
argument or subobject of the actual becomes undefined.

The value permitted for a {\it layout-spec} is {\tt C_ARRAY}.

If no {\it layout-spec} is specified for a dummy array argument, the array
element order shall be the same as that specified by Fortran.  If the value of
{\it layout-spec} specified is {\tt C_ARRAY}, the array element order of the
array shall be transposed for the duration of the reference to the procedure.

\begin{reviewers}
Note that we have no way of specifying {\it layout-spec} for structure
components.
\end{reviewers}

\subsection{Examples of Data Type Mappings}

Some examples should help to clarify what sorts of C procedure definitions
would be permitted given an interface body in a Fortran program.  For example,
the following interface body

\CODE
        INTERFACE
          EXTRINSIC('C') SUBROUTINE C_SUB(I, R, DARR, STRUCT)
            INTEGER, MAPTO('INT') :: I
            REAL, MAPTO('FLOAT', PASSBY='REF') :: R
            REAL(KIND(1.0D0)), MAPTO('DOUBLE') :: DARR(10)
            TYPE DT
              SEQEUNCE
              INTEGER :: I, J
            END TYPE DT
            TYPE(DT), MAPTO('(INT, LONG)', 'REF') :: STRUCT
          END SUBROUTINE C_SUB
        END INTERFACE
\EDOC

could correspond to a C procedure which has the prototype

\CODE
        void c_sub(int i, float r*, double darr[10], struct {int i, long j} *)
\EDOC

In the following example of the {\it layout-spec},

\CODE
      PROGRAM P
        INTERFACE
          EXTRINSIC('C') SUBROUTINE C_SUB(A, B)
            INTEGER, MAPTO('INT') :: A(2,2)
            INTEGER, MAPTO('INT', LAYOUT='C_ARRAY') :: B(2,2)
          END SUBROUTINE C_SUB
        END INTERFACE

        INTEGER :: AA(2,2), BB(2,2)
        CALL C_SUB(AA, BB)
      END PROGRAM P

      void c_sub(int a[2][2], b[2][2])
\EDOC

the correspondence between elements of {\tt AA} and {\tt a}, and elements of
{\tt BB} and {\tt b} is

\CODE
        AA(1,1)   a[0][0]              BB(1,1)   b[0][0]
        AA(2,1)   a[0][1]              BB(2,1)   b[1][0]
        AA(1,2)   a[1][0]              BB(1,2)   b[0][1]
        AA(2,2)   a[1][1]              BB(2,2)   b[1][1]
\EDOC

\end{document}
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% File: portable.tex

% Contents:
% Portable and Efficient Constructs chapter for HPF 2.0 document,
% including 
%	Kernel HPF
%	FORALL examples

% Revision history:
% May-10-96	Created by Andy Meltzer, Cray Research
%		(who thought it was ``Kernel HPF'')
% July-?-96	(Meltzer) Cleaned it up when found out it was only a chapter.
% Aug-7-96	(Meltzer) updated based on comments by Schreiber.



\chapter{Portable and Efficient Constructs}
\label{ch-portable}


{\em
Comments on this chapter should be directed to 
Andy Meltzer ({\tt meltzer@cray.com}),
Chuck Koelbel ({\tt chk@cs.rice.edu}),
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Portable/Efficient}'' as the {\tt Subject:}
line.
\par
}



%  {Coding for Portable Performance in HPF}
%  {Ver 1.0}
%  {Andrew Meltzer}
%  {Cray Research, Inc.}
%  {April, 1996}


%\section{Introduction}


The aim of this chapter is to identify a set of features that will provide
portable high performance.
It identifies a specific set of directives
and paradigms that are particularly easy to use.  This set compiles to an
efficient parallel program on most machines.  

HPF 2.0 includes many features that offer ease of use, but
the excessive overhead associated with the implementation of these features
can severely
compromise performance on one or more (even all for some combination
of features) distributed memory parallel computers.  
This kernel set of features is often referred to as the {\em HPF Kernel}.

The HPF Kernel is a high performance subset of HPF 2.0.  The features chosen
were selected for the following reasons
\begin{itemize}
\item They allow high-performance across all platforms.
\item On no platform are there performance ``surprises,''  Few, if any,
      combinations
      of the portable, high-performance features unexpectedly lead
      the user into low-performance
      circumstances although it is still possible for application
      programmers to write low-performance codes and for vendors to
      provide low-performance implementations.
\item They are easily understood.
\item They are commonly used.
\item They are valuable for all platforms.
\end{itemize}

HPF Kernel features
simplify the HPF model by reducing the variety of mappings to
only those most commonly used.    These features also
remove a level of abstraction.  The kernel features
might be a good place to begin learning to program in HPF.

The use of these features does not guarantee a high-performance application,
but these features increase the likelyhood that an application will get the
most out of the HPF language.   These features are also described here to
assist the user with an understanding of the sorts of operations that can
be efficiently executed.  Many vendors will have implemented many more
features that execute efficiently, a description of these is available
with the vendor's implementation.

The chapter is organized by HPF feature.  Features are listed and described
as restricted, not recommended, or recommended.   Restrictions are described.

\section{The {\tt {DISTRIBUTE}} Directive}

The {\tt {DISTRIBUTE}} directive remains mostly intact, only a few pieces
of functionality are not suggested when trying to achieve portable performance.
\subsection{Distribution Formats}

The HPF Kernel includes only the {\tt {BLOCK}} and {\tt {CYCLIC}} and
on-processor distributions.  It does
not include the {\tt {CYCLIC(N)}}, or {\tt {BLOCK(N)}}
distributions.  The effort to determine the locations of the elements
in an array with the {\tt {BLOCK}} and {\tt {CYCLIC}} distribution
is much less than the parameterized distributions.

\subsection{On-Processor Dimensions}
The ``*'' syntax is included in the {\tt {DISTRIBUTE}} directive
{\em {dist-format-clause}} to indicate on-processor dimensions.

This is a convenient technique for increasing locality of
reference, a goal for most high performance codes.  It can be accomplished
efficiently with reasonable compiler effort.

\section{\tt {DYNAMIC} Distributions}

The {\tt {DYNAMIC}} attribute is not recommended for portable
high-performance coding.   These distributions have obvious merit and
certain applications may require their general capabilities,  but
because of the inherent dynamic overhead required on even the most
advanced implementations, they cannot be recommended as high-performance
features.

\section{The {\tt {PROCESSORS}} Directive}

The {\tt {PROCESSORS}} directive is part of the HPF Kernel
with the following restrictions:
\begin{itemize}
\item The product of the extents must exactly match the number of
      processors or the processor arrangement must be scalar.
\item If an {\tt {ONTO}} clause is not specified, a default
      arrangement is provided which is identical for distributees
      that have identical shapes and identical explicit mappings.
\end{itemize}

If a processors directive is not specified a default arrangement is
provided which is identical for arrays that have identical shapes,
bounds, and identical explicit mapping directives.


\section{The {\tt {ALIGN}} Directive}

In The HPF Kernel the {\tt {ALIGN}} directive is restricted to
alignments that are direct;  there may be no offsets or strides
within an  {\tt {ALIGN}}.
Replication and collapse of dimensions is allowed.
In alignment expressions the dimensions may not be permuted.

\begin{itemize}
\item   Alignments may not contain offsets or strides.
\item   The {\em {align-subscript-use}} in the HPF 1.1 syntax rules should be
        replaced with {\em {align-dummy}}.

\item   Dimensions may not be permuted.

\item   A `*' is allowed either in the align-spec or in the alignee.
\end{itemize}

For example the following is code will likely execute efficiently:

        {\tt {CHPF\$           ALIGN A(I,J) WITH B(I,J)}}

But the following may not:

        {\tt {CHPF\$           ALIGN A(I,J) WITH B(I+1,J)}}


Offsets are not suggested for the {\tt {ALIGN}} directive when coding
for portable high-performance.  The effect of offsets can be
often be achieved by changing the bounds of arrays.
The following two examples will create the same alignment.

    {\em {Example 2a}}
\begin{verbatim}
                DIMENSION A(1:100), B(0:99)
        CHPF$   PROCESSORS P(32)
        CHPF$   DISTRIBUTE B(BLOCK) ONTO P
        CHPF$   ALIGN A(I) WITH B(I-1)  ! Disallowed
\end{verbatim}

    {\em {Example 2b}}
\begin{verbatim}
                DIMENSION A(1:100), B(0:99)
        CHPF$   PROCESSORS P(32)
        CHPF$   DISTRIBUTE A(BLOCK) ONTO P
        CHPF$   DISTRIBUTE B(BLOCK) ONTO P
\end{verbatim}

\section{The {\tt {TEMPLATE}} Directive}

The {\tt {TEMPLATE}} directive itself needs no restriction, but the use of
templates is restricted by the changes to the {\tt {ALIGN}} directive.


\section{The Reduction Clause in the {\tt INDEPENDENT} Directive}

The reduction clause in the {\tt INDEPENDENT} directive
may be used when coding for portable
high-performance.  The directive
only pertains to intrinsic operators and types.

\section{The {\tt {FORALL}} Statement and Construct}

Both the {\tt FORALL} statement and construct are recommended for
use when coding for portable high-performance.

{\tt {FORALL}} is a powerful and expressive way
to code parallelism.  It is true that not all {\tt {FORALL}}
statements and/or constructs can be fully parallelized, but because
of their general value and because they will be part of Fortran 95,
they are included in the HPF Kernel.

\section{{\tt {PURE}} Functions and Subroutines}

These are recommended for use when coding for portable high-performance.
{\tt {PURE}} functions can do no harm, and allow
an increased level of expressiveness.  They simplify the job for
the compiler and are part of Fortran 95.

\section{The {\tt {INDEPENDENT}} Directive}

The {\tt {INDEPENDENT}} directive is recommended for portable
high-performance, but with some caveats.  The {\tt {INDEPENDENT}}
directive gives a user access to facilities otherwise not available
by any means.  It can be abused, however, and not all implementations
may be able to handle all combinations of function calls within
{\tt INDEPENDENT} loops.  Care must be taken when exploiting this
feature.

Directives such as {\tt {INDEPENDENT}} have shown
their worth historically across a broad variety of platforms.  This
directive simplifies the analysis the compiler must do and can inform
the compiler about optimizations that it may do that otherwise
are expensive or impossible to deduce.   {\tt {INDEPENDENT}} allows
an increased level of optimization.

\section{Extrinsics and {\tt {HPF\_LOCAL}} and {\tt {HPF\_SERIAL}} }

The general purpose extrinsic mechanism, {\tt {HPF\_LOCAL}} and
{\tt {HPF\_SERIAL}} are all recommended for use when coding for
portable high-performance.

These allow a program to get at the highest performing features of a
particular architecture.


\section{Library}

All of the HPF 1.1 library routines are recommended for use when
coding for portable high-performance.  The intrinsics provide fast,
architecture specific
versions of many very important parallel functions.  To achieve a
similar level of performance for these functions a user would have
to write non-portable code.


\section{The {\tt {INHERIT}} Directive}

The  {\tt {INHERIT}} directive is recommended for use when coding
for portable high-performance.
The {\tt {INHERIT}} directive is not a high-performance
feature, but its impact can be isolated to the few places where it is
very useful.  The {\tt {INHERIT}} directive can be instrumental when
coding library and general purpose routines.

Care must be taken when using this directive as it is only a convenience
feature, not a high-performance feature.


\section{Pointers}

When coding for portable high-performance it is recommended that a
given pointer only point to identically explicitly mapped objects.


\section{Subroutine Interfaces}

Explicit interfaces are recommended for any subroutine
which remaps data.  This gives the language processor the necessary
means (without interprocedural optimizations) to remap data at
the call site statically, rather than dynamically at the callee.
Dummy arguments from actual argument array sections cannot be
mapped ``{\tt {DISTRIBUTE * ONTO *}}.'' Non-unit
strides may be specified when passing array sections as actual
arguments.

Assumed shape explicitly mapped dummies  may be used,
but explicit interfaces must be included where ever
they are used. Assumed shape dummies may use any mapping syntax.
The results of array valued functions may be explicitly mapped.  Assumed
size arrays are not recommended.

An explicit interface is required in the following cases:

\begin{itemize}

\item The dummy argument has the {\tt {INHERIT}} attribute.
\item  The mapping of a dummy argument is not the same as the mapping of
the corresponding actual argument, and at least one of the following
two conditions is true:

\begin{enumerate}
        \item the dummy argument is explicitly mapped;

        \item the actual argument is an explicitly mapped whole array or
           a section of an explicitly mapped array.
\end{enumerate}

\end{itemize}



Much better control of the remapping can be achieved
if the explicit interface is available and much less code to check
mappings and remap upon entry is necessary.

\section{Storage and Sequence Association}

It is not recommended that storage or sequence association be relied
upon when coding for portable performance.
The {\tt SEQUENCE} directive is not suggested.  This means that the user
should not use equivalence, common blocks must be declared identically
everywhere, and no arguments may be passed with mismatched shapes.




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From: Mary E Zosel <zosel@coral.llnl.gov>
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% File: credits.tex

% Contents:
% Acknowledgments for HPF 2.0 document

% Revision history:
% May-10-96	Created by Charles Koelbel, Rice University
%		(copied from HPF 1.1 document)
% Aug-9-96	Mary Zosel - separate out HPF2 from older stuff (to appendix)



\chapter*{Acknowledgments}


{\em
Comments on this chapter should be directed to 
Mary Zosel ({\tt zosel@llnl.gov}),
Charles Koelbel ({\tt chk@cs.rice.edu}),
and {\tt hpff-doc@cs.rice.edu}.

Please use ``{\tt Comments on Acknowledgments}'' as the {\tt Subject:}
line.
}

The High Performance Fortran Forum (HPFF) is a coalition of
industrial and academic groups working to suggest a set of standard
extensions to Fortran to provide the necessary information.  Its intent
is to develop extensions to Fortran that provide support for high
performance programming on a wide variety of machines, including
massively parallel SIMD and MIMD systems and vector processors.  From
its beginning, HPFF has included most vendors delivering parallel machines,
a number of government laboratories, and university research
groups.  Public input has been encouraged.
This document defining HPF 2.0 is the third in a series of documents 
resulting from the HPFF project.  
HPF 2.0 is  intended to be a language
specification portable from workstations to massively parallel
supercomputers while being able to express the algorithms needed to
achieve high performance on specific architectures. HPF 2.0 builds on the 
efforts of the previous HPFF meetings, primarily in 1992 and 1994.  Specific acknowlegments for the many people who contributed to the previous versions of
HPF are included in appendix \ref{old-ack}.  


\section{HPFF 2 Acknowledgments}
\label{hpff2-ack}

The HPF 2.0 version of the document was prepared during 
series of meetings in 1995-1996. 
A number of people shared technical  responsibilities for
the activities of these  meetings:

\begin{itemize}

\item Ken Kennedy, Convener and Meeting Chair;

\item Mary Zosel, Executive Director;

\item Rob Schreiber, Organizer for Control Subgroup;

\item Piyush Mehrotra and Guy Steele, Organizers for Distribution Subgroup;

\item David Loveman, Organizer for External Subgroup;

\item  Chuck Koelbel, Editor, assisted by a hoard of screaming
extras. Plus more (screaming)
names will be listed here after we determine who does
the work.

\end{itemize}

Attendence at the HPFF 2 meetings included the following people from
organizations that were represented two or more times.


%Attendee \hfill Organization

John Levesque, Marc Baber   \dotfill Applied Parallel Research \hspace{.125in}

Ian Foster   \dotfill Argonne National Laboratory \hspace{.125in}

Jaspal Subhlok   \dotfill Carneigie Mellon \hspace{.125in}

Jim Cowie \dotfill  Cooperating Systems \hspace{.125in}

Andy Meltzer \dotfill Cray Research
\hspace{.125in}

Henk Sipps, Will Denissen   \dotfill Delft University of Tech. \hspace{.125in}

David Loveman, Carl Offner \dotfill  Digital Equipment Corporation
\hspace{.125in}

Joel Williamson \dotfill Hewlett Packard/Convex \hspace{.125in}

Henry Zongaro  \dotfill  IBM \hspace{.125in}

Piyush Mehrotra \dotfill
Institute for Computer Applications in Science
\& Engineering \hspace{.125in}

Mary Zosel  \dotfill
Lawrence Livermore National Laboratory \hspace{.125in}

Robert Boland, Ralph Brickner, Joe Fasel \dotfill Los Alamos National Laboratory \hspace{.125in}

J. Ramanujam, Arun Venkatachar \dotfill Louisiana State University \hspace{.125in}

Steve Hammond   \dotfill National Center for Atmospheric Research  \hspace{.125in}

Yoshiki Seo \dotfill  NEC \hspace{.125in}

P. Sadayappan,  \dotfill  Ohio State University
\hspace{.125in}

Larry Meadows, Zeki Bozkus \dotfill  The Portland Group, Inc.
\hspace{.125in}

Robert Schreiber \dotfill
Research Institute for Advanced Computer Science / HP \hspace{.125in}

Ken Kennedy, Charles Koelbel \dotfill  Rice University \hspace{.125in}

Alok Choudhary, Hon Yau, Tom Haupt
\dotfill  Syracuse University \hspace{.125in}

Guy Steele  \dotfill  Sun MicroSystems
\hspace{.125in}

Paula Vaughn  \dotfill Mississippi State  \hspace{.125in}

Carol Munroe, Harvey Richardson \dotfill
Thinking Machines Corp. \hspace{.125in}

Scott Baden, Steve Fink, Jay Boisseau \dotfill
University of California, San Diego \hspace{.125in}

Robert Babb  \dotfill   University of Denver \hspace{.125in}

Joel Saltz, Paul Havlak, Manuel Ujaldon  \dotfill University of Maryland \hspace{.125in}

Jerrold Wagener  \dotfill X3J3, University of Oklahoma
\hspace{.125in}

Barbara Chapman, Siegfried Benkner, Guy Robinson \dotfill University of
Vienna \hspace{.125in}

An important activity of HPFF 2 meetings was the processing of the many items
submitted for comment, correction, and interpretation.   A general thanks goes to all
who submitted comments and interpretation requests.  The following people
submitted items that resulted in changes to the document text: 
Yasuharu Hayashi,
Michael Hennecke, 
Larry Meadows, 
Eiji Nunohiro, 
Carl Offner,
Rob Schreiber,
David Singleton,
Shigeru Uzuhara,
Clint Whaley,
and, last, but most prolific - 
Henry Zongaro.


Other special mention goes to  Chuck Koelbel at
Rice University for continued
maintenance of the HPFF mailing lists.

Theresa Chatman and staff at Rice University were responsible for
meeting planning and organization and Danny Powell
continued to handle financial details of the project.

HPFF  2 received direct support for research and administrative
activities from grants from ARPA, DOE, and NSF.

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% File: oldack-app.tex

% Contents:
% Old  HPF Acknowlegements Appendix for HPF 2.0 document

% Revision history:
% Aug-1l-96     Created by Mary Zosel, LLNL
%               (from HPF 1.1 document)



\chapter{Previous HPFF Acknowledgments}
\label{oldack-app}


{\em
Comments on this chpater should be directed to
Mary Zosel ({\tt zosel@llnl.gov})
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Old Credits HPF}'' as
the {\tt Subject:} line.
\par
}

The current HPF 2.0 document would not have been possible without
the contributions of the previous series of HPFF meetings.  Following
are the acknowlegements for those efforts.

\section{HPFF Acknowledgements}
\label{hpff-ack}

Technical development for HPF 1.0  was carried out by subgroups, and
was reviewed by the full committee.  Many people served in positions of 
responsibility:

\begin{itemize}

\item Ken Kennedy, Convener and Meeting Chair;

\item Charles Koelbel, Executive Director and Head of the FORALL Subgroup;

\item Mary Zosel, Head of the Fortran 90 and Storage Association Subgroup;

\item Guy Steele, Head of the Data Distribution Subgroup;

\item Rob Schreiber, Head of the Intrinsics Subgroup;

\item Bob Knighten, Head of the Parallel I/O Subgroup;

\item Marc Snir, Head of the Extrinsics Subgroup;

\item Joel Williamson and Marina Chen, Heads of the Subroutine 
Interface Subgroup; and

\item David Loveman, Editor.

\end{itemize}



Geoffrey Fox convened the first HPFF meeting with Ken Kennedy and
later led a group to develop benchmarks for HPF.  
Clemens-August Thole organized a  group in Europe and was
instrumental in making this an international effort.  Charles Koelbel
produced detailed meeting  minutes
that were invaluable to
subgroup heads in preparing successive revisions to the draft
proposal.  Guy Steele developed \LaTeX\ macros for a variety of tasks, 
including formatting BNF grammar, Fortran code and pseudocode, and 
commentary material; the document would have been much less aesthetically 
pleasing without his efforts.

Many companies, universities, and other entities supported their
employees' attendance at the HPFF meetings, both directly and
indirectly.  The following organizations were represented at two or
more meetings by the following individuals (not including those present
at the first HPFF meeting in January of 1992, for which there is no 
accurate attendee list):

%Organization \hfill Attendee 
Alliant Computer Systems Corporation \dotfill  David Reese
\hspace{.125in}

Amoco Production Company  \dotfill  Jerrold Wagener, Rex Page
\hspace{.125in}

Applied Parallel Research  \dotfill John Levesque, Rony Sawdayi, Gene
Wagenbreth  \hspace{.125in}

Archipel  \dotfill  Jean-Laurent Philippe \hspace{.125in}

CONVEX Computer Corporation  \dotfill  Joel Williamson \hspace{.125in}

Cornell Theory Center  \dotfill  David Presberg \hspace{.125in}

Cray Research, Inc.  \dotfill  Tom MacDonald, Andy Meltzer
\hspace{.125in}

Digital Equipment Corporation  \dotfill  David Loveman
\hspace{.125in}

Fujitsu America \dotfill  Siamak Hassanzadeh, Ken Muira \hspace{.125in}

Fujitsu Laboratories \dotfill Hidetoshi Iwashita \hspace{.125in}

GMD-I1.T, Sankt Augustin  \dotfill  Clemens-August Thole
\hspace{.125in}

Hewlett Packard  \dotfill  Maureen Hoffert, Tin-Fook Ngai, Richard
Schooler \hspace{.125in}

IBM  \dotfill  Alan Adamson, Randy Scarborough, Marc Snir, Kate Stewart
\hspace{.125in}

Institute for Computer Applications in Science \& Engineering  \dotfill
    Piyush Mehrotra \hspace{.125in} 

Intel Supercomputer Systems Division  \dotfill  Bob Knighten
\hspace{.125in}

Lahey Computer  \dotfill  Lev Dyadkin, Richard Fuhler, Thomas Lahey,
Matt Snyder \hspace{.125in}

Lawrence Livermore National Laboratory  \dotfill  Mary Zosel
\hspace{.125in}

Los Alamos National Laboratory  \dotfill  Ralph Brickner, Margaret
Simmons \hspace{.125in}

Louisiana State University  \dotfill  J. Ramanujam \hspace{.125in}

MasPar Computer Corporation  \dotfill  Richard Swift \hspace{.125in}

Meiko, Inc.  \dotfill  James Cownie \hspace{.125in}

nCUBE, Inc.  \dotfill  Barry Keane, Venkata Konda \hspace{.125in}

Ohio State University  \dotfill  P. Sadayappan \hspace{.125in}

Oregon Graduate Institute of Science and Technology  \dotfill  Robert
Babb II \hspace{.125in}

The Portland Group, Inc.  \dotfill  Vince Schuster \hspace{.125in}

Research Institute for Advanced Computer Science  \dotfill  Robert
Schreiber \hspace{.125in}

Rice University  \dotfill  Ken Kennedy, Charles Koelbel \hspace{.125in}

Schlumberger  \dotfill  Peter Highnam \hspace{.125in}

Shell  \dotfill  Don Heller \hspace{.125in}

State University of New York at Buffalo  \dotfill  Min-You Wu
\hspace{.125in}

SunPro and Sun Microsystems  \dotfill  Prakash Narayan, Douglas Walls
\hspace{.125in}

Syracuse University  \dotfill  Alok Choudhary, Tom Haupt
\hspace{.125in}

TNO-TU Delft  \dotfill  Edwin Paalvast, Henk Sips \hspace{.125in}

Thinking Machines Corporation  \dotfill  Jim Bailey, Richard Shapiro,
Guy Steele  \hspace{.125in}

United Technologies Corporation  \dotfill  Richard Shapiro
\hspace{.125in}

University of Stuttgart  \dotfill 
 Uwe Geuder, Bernhard Woerner, Roland Zink \hspace{.125in}

University of Southampton \dotfill John Merlin \hspace{.125in}

University of Vienna  \dotfill  Barbara Chapman, Hans Zima
\hspace{.125in}

Yale University  \dotfill  Marina Chen, Aloke Majumdar \hspace{.125in}

Many people contributed sections to the final 
language specification and HPF Journal of Development, including 
Alok Choudhary,
Geoffrey Fox,
Tom Haupt,
Maureen Hoffert,
Ken Kennedy,
Robert Knighten,
Charles Koelbel,
David Loveman,
Piyush Mehrotra,
John Merlin,
Tin-Fook Ngai,
Rex Page,
Sanjay Ranka,
Robert Schreiber,
Richard Shapiro,
Marc Snir,
Matt Snyder,
Guy Steele,
Richard Swift,
Min-You Wu,
and
Mary Zosel.
Many others contributed shorter passages and examples and corrected errors. 

Because public input was encouraged on electronic mailing lists, it is
impossible to identify all who contributed to
discussions;  the entire mailing list was over 500 names
long. Following are  some of the active participants in
the HPFF process not mentioned above:

\begin{centering}

\begin{tabular}{lll}
N. Arunasalam &
Werner Assmann &
Marc Baber \\
Babak Bagheri &
Vasanth Bala &
Jason Behm \\
Peter Belmont &
Mike Bernhardt &
Keith Bierman \\
Christian Bishof &
John Bolstad &
William Camp \\
Duane Carbon & 
Richard Carpenter &
Brice Cassenti \\
Doreen Cheng &
Mark Christon &
Fabien Coelho \\
Robert Corbett &
Bill Crutchfield &
J. C. Diaz \\
James Demmel &
Alan Egolf &
Bo Einarsson \\
Pablo Elustondo &
Robert Ferrell &
Rhys Francis \\
Hans-Hermann Frese &
Steve Goldhaber &
Brent Gorda \\
Rick Gorton &
Robert Halstead &
Reinhard von Hanxleden \\
Hiroki Honda &
Carol Hoover &
Steven Huss-Lederman \\
Ken Jacobsen &
Elaine Jacobson &
Behm Jason \\
Alan Karp &
Ronan Keryell &
Anthony Kimball \\
Ross Knippe &
Bruce Knobe &
David Kotz \\
Ed Krall &
Tom Lake &
Peter Lawrence \\
Bryan Lawver &
Bruce Leasure &
Stewart Levin \\
David Levine &
Theodore Lewis &
Woody Lichtenstein \\
Ruth Lovely &
Doug MacDonald &
Raymond Man \\
Stephen Mark &
Philippe Marquet &
Jeanne Martin \\
Oliver McBryan &
Charlie McDowell &
Michael Metcalf \\ 
Charles Mosher &
Len Moss &
Lenore Mullin \\
Yoichi Muraoka &
Bernie Murray &
Vicki Newton \\
Dale Nielsen &
Kayutov Nikolay &
Steve O'Neale \\
Jeff Painter &
Cherri Pancake &
Harvey Richardson \\
Bob Riley &
Kevin Robert &
Ron Schmucker \\
J.L. Schonfelder &
Doug Scofield &
David Serafini \\
G.M. Sigut &
Anthony Skjellum &
Niraj Srivastava \\
Paul St.Pierre &
Nick Stanford &
Mia Stephens \\
Jaspal Subhlok &
Xiaobai Sun &
Hanna Szoke \\
Bernard Tourancheau &
Anna Tsao &
Alex Vasilevsky \\
Stephen Vavasis &
Arthur Veen &
Brian Wake \\
Ji Wang &
Karen Warren &
D.C.B. Watson \\
Matthijs van Waveren &
Robert Weaver &
Fred Webb \\
Stephen Whitley &
Michael Wolfe &
Fujio Yamamoto \\
Marco Zagha 

\end{tabular}

\end{centering}

The following organizations made the language draft available by anonymous FTP 
access and/or mail servers:
AT\&T Bell Laboratories,
Cornell Theory Center,
GMD-I1.T (Sankt Augustin), 
Oak Ridge National Laboratory,
Rice University,
Syracuse University,
and Thinking Machines Corporation.
These outlets were instrumental in distributing the document.

The High Performance Fortran Forum also received a great deal of
volunteer effort in nontechnical areas.  Theresa Chatman and Ann
Redelfs were responsible for most of the meeting planning and
organization, including the first HPFF meeting, which drew over 125
people.  Shaun Bonton, Rachele Harless, Rhonda Perales, Seryu Patel, and 
Daniel Swint
helped with many logistical details.  Danny Powell spent a great deal
of time handling the financial details of the project.  Without these
people, it is unlikely that HPF would have been completed.

HPFF operated on a very tight budget (in reality, it had no budget when
the first meeting was announced).  The first meeting in Houston was
entirely financed from the conferences budget of the Center for
Research on Parallel Computation, an NSF Science and Technology
Center.  DARPA and NSF have supported research at various institutions
that have made a significant contribution towards the development of
High Performance Fortran.  Their sponsored projects at Rice, Syracuse,
and Yale Universities were particularly influential in the HPFF
process.  Support for several European participants was provided by
ESPRIT  through projects P6643 (PPPE) and P6516 (PREPARE).  
%{\it Mention anybody else who gave us money here.}


\section{HPFF94 Acknowledgements}
\label{hpff94-ack}

The HPF 1.1 version of the document was prepared during the HPFF94
series of meetings. A number of people shared technical  responsibilities for
the activities of the HPFF94 meetings:

\begin{itemize}

\item Ken Kennedy, Convener and Meeting Chair;

\item Mary Zosel, Executive Director and head of CCI Group 2;

\item Richard Shapiro, Head of CCI Group 1;

\item Ian Foster, Head of Tasking Subgroup;

\item Alok Choudhary, Head of Parallel I/O Subgroup;

\item Chuck Koelbel, Head of Irregular Distributions Subgroup;

\item Rob Schreiber, Head of Implementation Subgroup;

\item Joel Saltz, Head of Benchmarks Subgroup;

\item David Loveman, Editor, assisted by Chuck Koelbel,
Rob Schreiber, Guy Steele,
and Mary Zosel, section editors.

\end{itemize}

Attendence at the HPFF94 meetings included the following people from
organizations that were represented two or more times.


%Attendee \hfill Organization
Don Heller  \dotfill  Ames Laboratory \hspace{.125in}

Jerrold Wagener  \dotfill  Amoco Production Company
\hspace{.125in}

John Levesque   \dotfill Applied Parallel Research \hspace{.125in}

Ian Foster   \dotfill Argonne National Laboratory \hspace{.125in}

Terry Pratt \dotfill  CESDIS/NASA Goddard \hspace{.125in}

Jim Cowie \dotfill  Cooperating Systems \hspace{.125in}

Andy Meltzer, Jon Steidel \dotfill Cray Research, Inc. 
\hspace{.125in}

David Loveman \dotfill  Digital Equipment Corporation 
\hspace{.125in}

Bruce Olsen \dotfill Hewlett Packard \hspace{.125in}

E. Nunohiro, Satoshi Itoh \dotfill  Hitachi \hspace{.125in}

Henry Zongaro  \dotfill  IBM \hspace{.125in}

Piyush Mehrotra \dotfill 
Institute for Computer Applications in Science
\& Engineering \hspace{.125in}

Bob Knighten, Roy Touzeau \dotfill  Intel SSD  
\hspace{.125in}

Mary Zosel, Bor Chan, Karen Warren \dotfill  
Lawrence Livermore National Laboratory \hspace{.125in}

Ralph Brickner \dotfill Los Alamos National Laboratory \hspace{.125in}

J. Ramanujam \dotfill Louisiana State University \hspace{.125in}

Paula Vaughan, Donna Reese \dotfill 
Miss. State University / NSF ERC \hspace{.125in}

Shoichi Sakon, Yoshiki Seo\dotfill  NEC \hspace{.125in}

P. Sadayappan, Chua-Huang Huang \dotfill  Ohio State University
\hspace{.125in}

Andrew Johnson \dotfill  OSF Research Institute \hspace{.125in}

Chip Rodden, Jeff Vanderlip \dotfill Pacific Sierra Research
\hspace{.125in}

Larry Meadows, Doug Miles \dotfill  The Portland Group, Inc.
\hspace{.125in}

Robert Schreiber \dotfill  
Research Institute for Advanced Computer Science \hspace{.125in}

Ken Kennedy, Charles Koelbel \dotfill  Rice University \hspace{.125in}

Ira Baxter \dotfill  Schlumberger \hspace{.125in}

Alok Choudhary
 \dotfill  Syracuse University \hspace{.125in}

Guy Steele  \dotfill  Thinking Machines Corporation, Sun MicroSystems
\hspace{.125in}

Richard Shapiro \dotfill 
 Thinking Machines Corp., Silicon Graphics Inc. \hspace{.125in}

Scott Baden, Val Donaldson\dotfill 
University of California, San Diego \hspace{.125in}

Robert Babb  \dotfill   University of Denver \hspace{.125in}

Joel Saltz, Paul Havlak \dotfill University of Maryland \hspace{.125in}

Nicole Nemer-Preece \dotfill  University of
Missouri-Rolla \hspace{.125in}

Hans Zima, Siegfried Benkner, Thomas Fahringer \dotfill University of
Vienna \hspace{.125in}

An important activity of HPFF94 was the processing of the many items
submitted for comment and interpretation which led to the HPF 1.1
update of the language document.  A special acknowlegement
goes to Henry Zongaro, IBM, for many thoughtful questions 
exposing dark corners of language design that 
were previously overlooked, and to
Guy Steele, Thinking Machines/Sun Microsystems for his analysis
of, and solutions for some of the thornier issues discussed.
And general thanks to the people who submitted comments and
interpretation requests, including:

David Loveman, Michael Hennecke, James Cownie,
Adam Marshall, Stephen Ehrlich, Mary Zosel, Matt Snyder,
Larry Meadows, Dick Hendrickson,
Dave Watson, John Merlin, Vasanth Bala, Paul.Wesson,
Denis.Hugli, Stanly Steinberg, Henk Sips, Henry Zongaro,
Eiji_Nunohiro, Jens Bloch Helmers, Rob Schreiber, 
David B. Serafini, and Allan Knies.

Other special mention goes to  Chuck Koelbel at
Rice University for continued 
maintenance of the HPFF mailing lists, to Donna Reese and staff at
Mississippi State University for establishing and maintaining a
WWW home-page for HPFF,
and to the University of Maryland for
establishing a benchmark FTP site.

Theresa Chatman and staff at Rice University were responsible for
meeting planning and organization and Danny Powell 
continued to handle financial details of the project.

HPFF94 received direct support for research and administrative
activities from grants from ARPA, DOE, and NSF.


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% File: mapping-base.tex

% Contents:
% Mapping constructs for local variables for HPF 2.0 document,
% including
%       DISTRIBUTE
%       ALIGN
%       SEQUENCE
%       some of pointer mappings
%       equivalence of mappings


% Revision history:
% May-10-96     Created by Charles Koelbel, Rice University
%               (from HPF 1.1 document and HPF 2.0 proposals)
% May-22-96     Chapter updated by Piyush Mehrotra
%



\chapter{Data Mapping}
\label{ch-mapping-base}

{\em
Comments on this chapter should be directed to 
Piyush Mehrotra ({\tt pm@icase.edu}), 
Carl Offner ({\tt offner@hpc.pko.dec.com}), 
Guy Steele ({\tt Guy.Steele@east.sun.com})
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Mapping}'' as the {\tt Subject:}
line.
\par
}
  {\em This chapter is based on the old chapter on Data Mappings.
I have removed all references to dynamic remapping of data
({\tt DYNAMIC, REDISTRIBUTE} and {\tt REALIGN}),
including those in the model section. Also
removed all references to mapping of aggregate covers 
and sequential objects from t eh section on storage and sequence association.
I have also replaced all
references to Fortran 90 with plain Fortran. -- PM}



HPF data alignment and distributions directives allow the
programmer to advise the compiler
how to assign array elements to processor memories.
This chapter discusses the basic data mapping features applicable,
particularly those that are meaningful within a single scoping unit.
Chapter~\ref{ch-mapping-subr} will discuss mapping features that apply
when mapped variables are passed as subprogram arguments.

\section{Model}

HPF adds directives to Fortran to allow the user to advise the
compiler on the allocation of data objects to processor memories.  The
model is that there is a two-level mapping of data objects to memory
regions, referred to as ``abstract processors.''  Data objects
(typically array elements) are first {\it aligned} relative to one
another; this group of arrays is then {\it distributed} onto a
rectilinear arrangement of abstract processors.  (The implementation
then uses the same number, or perhaps some smaller number, of physical
processors to implement these abstract processors.  This mapping of
abstract processors to physical processors is
implementation-dependent.)

The following diagram illustrates the model:

\begin{center}

\setlength{\unitlength}{0.01in}
\begin{picture}(600,240)(0,30)
\thicklines
\put(100,150){\circle{50}}
\put(242,150){\circle{50}}
\put(383,150){\circle{50}}
\put(525,150){\circle{50}}
\put(125,150){\vector(1,0){92}}
\put(267,150){\vector(1,0){91}}
\put(408,150){\vector(1,0){92}}
\put(56,190){\shortstack{Arrays or\strut\\other objects\strut}}
\put(192,190){\shortstack{Group of\strut\\aligned objects\strut}}
\put(328,190){\shortstack{Abstract\strut\\processors as a\strut
                \\user-declared\strut\\Cartesian mesh\strut}}
\put(494,190){\shortstack{Physical\strut\\processors\strut}}
\put(150,100){\tt ALIGN}
\put(270,100){\tt DISTRIBUTE}
\put(400,50){\shortstack{Optional\strut\\implementation-\strut
                \\dependent\strut\\directive\strut}}
\end{picture}

\end{center}

The underlying assumptions are that an operation on two or more data
objects is likely to be carried out much faster if they all reside in
the same processor, and that it may be possible to carry out many
such operations concurrently if they can be performed on different
processors.

Fortran provides a number of features, notably array syntax, that
make it easy for a compiler to determine that many operations may be
carried out concurrently.  The HPF directives provide a way to inform
the compiler of the recommendation that certain data objects should
reside in the same processor: if two data objects are mapped (via the
two-level mapping of alignment and distribution) to the same abstract
processor, it is a strong recommendation to the implementation that
they ought to reside in the same physical processor.  There is also a
provision for recommending that a data object be stored in multiple
locations, which may complicate any updating of the object but makes
it faster for multiple processors to read the object.

There is a clear separation between directives that serve as
specification statements and directives that serve as executable
statements (in the sense of the Fortran standards).  Specification
statements are carried out on entry to a program unit, as
if all at once; only then are executable statements carried out.
(While it is often convenient to think of specification statements as
being handled at compile time, some of them contain specification
expressions, which are permitted to depend on run-time quantities
such as dummy arguments, and so the values of these expressions may
not be available until run time, specifically the very moment that
program control enters the scoping unit.)

The basic concept is that every array (indeed, every object) is created 
with {\em some\/} alignment to an entity, which in turn has {\em some\/} 
distribution onto {\em some\/} arrangement of abstract processors.  
If the specification statements contain
explicit specification directives specifying the alignment of an
array {\tt A} with respect to another array {\tt B}, then the
distribution of {\tt A} will be dictated by the distribution of {\tt
B}; otherwise, the distribution of {\tt A} itself may be specified
explicitly.  In either case, any such explicit declarative
information is used when the array is created.  

\begin{implementors}
This model gives a better picture of the actual amount of work that
needs to be done than a model that says ``the array is created in some
default location, and then realigned and/or redistributed if there is
an explicit directive.''  Using {\tt ALIGN} and {\tt DISTRIBUTE}
specification directives doesn't have to cause any more work at run
time than using the implementation defaults.
\end{implementors}

In the case of an allocatable object, we say that the object is
created whenever it is allocated.  Specification directives for
allocatable objects 
may appear in the
{\it specification-part} of a program unit, but take effect each time the
array is created, rather than on entry to the scoping unit.

Alignment is considered an {\em attribute\/} (in the Fortran sense)
of a data object.  If an object {\tt A} is aligned 
with an object {\tt B}, which in turn is already aligned
to an object {\tt C}, this is regarded as an alignment of {\tt A} with
{\tt C} directly, with {\tt B} serving only as an intermediary at the
time of specification.
We say that {\tt A} is {\it immediately aligned} with {\tt
B} but {\it ultimately aligned} with {\tt C}.  If an object is not
explicitly aligned with another object, we say that it is ultimately
aligned with itself.  The alignment relationships form a tree with
everything ultimately aligned to the object at the root of the tree;
however, the tree is always immediately ``collapsed'' so that every
object is related directly to the root.  

Every object which is the root of an alignment tree has an associated 
{\em template\/} or index space.  Typically, this template has the same 
rank and size in each dimension as the object associated with it.  (The 
most important exception to this rule is dummy arguments with the {\tt 
INHERIT} attribute, described in Section~\ref{INHERIT-SECTION}.)  
We often refer to ``the template for an array,'' which means the 
template of the object to which the array is ultimately aligned.  (When 
an explicit {\tt TEMPLATE} (see Section~\ref{TEMPLATE-SECTION}) is 
used, this may be simply the template to which the array is explicitly 
aligned.)
        
The {\em distribution\/} step of the HPF model technically applies to 
the template of an array, although because of the close relationship 
noted above we often speak loosely of the distribution of an array.  
Distribution partitions the template among a set of abstract processors 
according to a given pattern.  The combination of alignment (from arrays 
to templates) and distribution (from templates to processors) thus 
determines the relationship of an array to the processors; we refer to 
this relationship as the {\em mapping\/} of the array.  (These remarks 
also apply to a scalar, which may be regarded as having an index space 
whose sole position is indicated by an empty list of subscripts.)

Every object is created as if according to some complete set of
specification directives; if the program does not include complete
specifications for the mapping of some object, the compiler provides
defaults.  By default an object is not aligned with any other object;
it is ultimately aligned with itself.  The default distribution is
implementation-dependent, but must be expressible as explicit
directives for that implementation.  
Identically declared
objects need not be provided with identical default distribution
specifications; the compiler may, for example, take into account the
contexts in which objects are used in executable code.  The programmer
may force identically declared objects to have identical distributions
by specifying such distributions explicitly.  (On the other hand,
identically declared processor arrangements {\it are} guaranteed to
represent ``the same processors arranged the same way.''  This is
discussed in more detail in Section~\ref{PROCESSORS-SECTION}.)


Sometimes it is desirable to consider a large index space with
which several smaller arrays are to be aligned, but not to
declare any array that spans the entire index space.
HPF allows one to declare a {\tt TEMPLATE}, which is like an array
whose elements have no content and therefore occupy no storage;
it is merely an abstract index space that can be distributed and
with which arrays may be aligned.




An object is considered to be {\it explicitly mapped}
if it appears in an HPF mapping directive within the scoping
unit in which it is declared;  otherwise it is
{\it implicitly mapped}. A mapping directive is an {\tt ALIGN},
or {\tt DISTRIBUTE},  
or {\tt INHERIT}
directive, or any directive that confers an alignment, a
distribution, or the {\tt INHERIT} 
attribute.

{\em Question: how do we handle mapping directives which occur in the 
approved extensions, e.g., dynamic, redistribute, realign, range, etc.}




\section{Syntax of Data Alignment and Distribution Directives}

Specification directives in HPF have two forms: specification
statements, analogous to the {\tt DIMENSION} and {\tt ALLOCATABLE}
statements of Fortran;
and an attribute form analogous to type declaration statements
in Fortran using the ``{\tt ::}'' punctuation.

The attribute form allows more than one attribute to be described
in a single directive.  HPF goes beyond Fortran in not requiring
that the first attribute, or indeed any of them, be a type specifier.


                                                                        \BNF
combined-directive         \IS  combined-attribute-list :: combined-decl-list

combined-attribute         \IS  ALIGN align-attribute-stuff
                           \OR  DISTRIBUTE dist-attribute-stuff
                           \OR  INHERIT
                           \OR  TEMPLATE
                           \OR  PROCESSORS
                           \OR  DIMENSION ( explicit-shape-spec-list )
combined-decl-list       \IS hpf-entity [(explicit-shape-spec-list)]
                            \OR object-name
hpf-entity                       \IS processors-name
                            \OR template-name
                                                                        \FNB

The {\tt INHERIT} attribute is related to subroutine call conventions
and will be discussed in Section~\ref{ch-mapping-subr}.
\begin{constraints}

\item The same {\it combined-attribute} must not appear more 
than once in a given {\it combined-directive}.

\item If the {\tt DIMENSION} attribute appears in a {\it
combined-directive}, any entity to which it applies must be declared
with the HPF {\tt TEMPLATE} or {\tt PROCESSORS} type specifier.

\end{constraints}

The following rules constrain the declaration of various attributes,
whether in separate directives or in a combined-directive.

If the {\tt DISTRIBUTE} attribute is present, then every name declared in the
{\it combined-decl-list} is considered to be a {\it distributee} and is subject
to the constraints listed in section~\ref{DISTRIBUTE-SECTION}.

If the {\tt ALIGN} attribute is present, then every name declared in the
{\it entity-decl-list} is considered to be an {\it alignee} and is subject
to the constraints listed in section~\ref{ALIGN-SECTION}.

The HPF keywords {\tt PROCESSORS} and {\tt TEMPLATE} play the role of
type specifiers in declaring processor arrangements and templates.
The HPF keywords {\tt ALIGN}, {\tt DISTRIBUTE}, 
and {\tt INHERIT} play the role of attributes.  Attributes referring to
processor arrangements, to templates, or to entities with other types
(such as {\tt REAL}) may be combined in an HPF directive without
having the type specifier appear.

No entity may be given a particular attribute more than once.

Dimension information may be specified after an {\it hpf-entity} or in a
{\tt DIMENSION} attribute.  If both are present, the one after the
{\it object-name} overrides the {\tt DIMENSION} attribute (this is consistent
with the Fortran standard).  For example, in:
                                                                        \CODE
!HPF$ TEMPLATE,DIMENSION(64,64) :: A,B,C(32,32),D
                                                                        \EDOC
{\tt A}, {\tt B}, and {\tt D} are \( 64 \times 64 \) templates; {\tt C}
is \( 32 \times 32 \).

Directives mapping a variable must be in the same scoping unit
where the variable is declared.  




If a specification expression includes a reference to the value of
an element of an array specified in the same specification-part,
any explicit mapping or {\tt INHERIT} attribute for the array
must be completely specified in prior specification-directives.
(This restriction is inspired by and extends
section 7.1.6.2 of the Fortran standard, which states in part:
If a specification expression includes a reference to the value of
an element of an array specified in the same specification-part,
the array bounds must be specified in a prior declaration.)


A comment on asterisks: The asterisk character ``{\tt *}'' appears
in the syntax rules for HPF alignment and distribution directives
in three distinct roles:
\begin{itemize}
\item  When a lone asterisk appears as a member of a parenthesized
list, it indicates either a collapsed mapping, wherein many
elements of an array may be mapped to the same abstract processor,
or a replicated mapping, wherein each element of an array may be mapped
to many abstract processors.   See the syntax rules for {\it align-source}
and {\it align-subscript} (see Section \ref{ALIGN-SECTION})
and for {\it dist-format} (see Section \ref{DISTRIBUTE-SECTION}).

\item When an asterisk appears in an {\it align-subscript-use}
expression, it represents the usual integer multiplication operator.

\item When an asterisk appears before a left parenthesis ``{\tt (}''
or after the keyword {\tt WITH} or {\tt ONTO}, it indicates that the
directive constitutes an assertion about the {\it current} mapping
of a dummy argument on entry to a subprogram, rather than a request
for a {\it desired} mapping of that dummy argument.  This use of
the asterisk may appear {\it only} in directives that apply to
dummy arguments (see Chapter~\ref{ch-mapping-subr}).

\end{itemize}

The first two of these uses are discussed in this chapter.  The last
is a subprogram interface issue and will be detailed in
Chapter~\ref{ch-mapping-subr}.

\section{DISTRIBUTE Directive}
\label{DISTRIBUTE-SECTION}

The {\tt DISTRIBUTE} directive specifies a mapping of data objects
to abstract processors in a processor arrangement.
For example,
                                                                        \CODE
      REAL SALAMI(10000)
!HPF$ DISTRIBUTE SALAMI(BLOCK)
                                                                        \EDOC
specifies that the array {\tt SALAMI} should be distributed across
some set of abstract processors by slicing it uniformly into blocks of
contiguous elements.  If there are 50 processors, the directive
implies that the array should be divided into groups of 200 elements,
with {\tt SALAMI(1:200)} mapped to the first processor,
{\tt SALAMI(201:400)} mapped to the second processor, and so on.
If there is only one processor, the entire array is mapped to that processor
as a single block of 10000 elements.

The block size may be specified explicitly:
                                                                        \CODE
      REAL WEISSWURST(10000)
!HPF$ DISTRIBUTE WEISSWURST(BLOCK(256))
                                                                        \EDOC
This specifies that groups of exactly 256 elements should be
mapped to successive abstract processors.
(There must be at least \( \lceil 10000/256 \rceil = 40 \) abstract processors
if the directive is to be satisfied.  The fortieth processor
will contain a partial block of only 16 elements, namely
{\tt WEISSWURST(9985:10000)}.)

HPF also provides a cyclic distribution format:
                                                                        \CODE
      REAL DECK_OF_CARDS(52)
!HPF$ DISTRIBUTE DECK_OF_CARDS(CYCLIC)
                                                                        \EDOC
If there are 4 abstract processors,
the first processor will contain {\tt DECK_OF_CARDS(1:49:4)},
the second processor will contain {\tt DECK_OF_CARDS(2:50:4)},
the third processor will contain {\tt DECK_OF_CARDS(3:51:4)},
and the fourth processor will contain {\tt DECK_OF_CARDS(4:52:4)}.
Successive array elements are dealt out to successive abstract processors
in round-robin fashion.

Distributions may be specified independently for each dimension of a
multidimensional array:
                                                                        \CODE
      INTEGER CHESS_BOARD(8,8), GO_BOARD(19,19)
!HPF$ DISTRIBUTE CHESS_BOARD(BLOCK, BLOCK)
!HPF$ DISTRIBUTE GO_BOARD(CYCLIC,*)
                                                                        \EDOC
The {\tt CHESS_BOARD} array will be carved up into contiguous
rectangular patches, which will be distributed onto a two-dimensional
arrangement of abstract processors.  The {\tt GO_BOARD} array will have its
rows distributed cyclically over a one-dimensional arrangement of
abstract processors.  (The ``{\tt *}'' specifies that {\tt GO_BOARD} is not to
be distributed along its second axis; thus an entire row is to be
distributed as one object.  This is sometimes called ``on-processor''
distribution.)

The {\tt DISTRIBUTE} directive may appear only in the {\it specification-part}
of a scoping unit  
and can contain only a {\it specification-expr} as the
argument to a {\tt BLOCK} or {\tt CYCLIC} option.

Formally, the syntax of the {\tt DISTRIBUTE}
directive is:

                                                                        \BNF
distribute-directive       \IS  DISTRIBUTE distributee dist-directive-stuff

dist-directive-stuff       \IS  dist-format-clause [ dist-onto-clause ]
dist-attribute-stuff       \IS  dist-directive-stuff
                           \OR  dist-onto-clause

distributee                \IS  object-name
                           \OR  template-name

dist-format-clause         \IS  ( dist-format-list )
                           \OR  * ( dist-format-list )
                           \OR  *

dist-format                \IS  BLOCK  [ ( int-expr ) ]
                           \OR  CYCLIC [ ( int-expr ) ]
                           \OR  *

dist-onto-clause           \IS  ONTO dist-target

dist-target                \IS  processors-name
                           \OR  * processors-name
                           \OR  *
                                                                        \FNB

The full syntax is given here for completeness, however some of the
forms will only be discussed in Chapter~\ref{ch-mapping-subr}.  These
``interprocedural'' forms are:
\begin{itemize}
\item The last two options of rule~\ref{dist-format-clause-rule} (containing
the {\tt *} form)
\item The last two options of rule~\ref{dist-target-rule} (containing
the {\tt *} form)
\end{itemize}

\begin{constraints}
\item An {\it object-name} mentioned as a {\it distributee}
must be a simple name and not a subobject designator.

\item An {\it object-name} mentioned as a {\it distributee} may not
appear as an {\it alignee}.

\item An {\it object-name} mentioned as a {\it distributee} may not
have the {\tt POINTER} attribute.


\item If a {\it dist-format-list} is specified, its length must
equal the rank of each {\it distributee}.

\item If both a {\it dist-format-list} and a {\it processors-name} appear, the
number of elements of the {\it dist-format-list} that are not ``{\tt *}''
must equal the rank of the named processor arrangement.

\item If a {\it processors-name} appears but not a {\it dist-format-list}, the
rank of each {\it distributee}
must equal the rank of the named processor arrangement.

\item If either the {\it dist-format-clause} or the {\it dist-target}
in a {\tt DISTRIBUTE} directive begins with ``{\tt *}'' then every {\it distributee}
must be a dummy argument.

\item Any {\it int-expr} appearing in a {\it dist-format} of a
{\tt DISTRIBUTE} directive must be a {\it specification-expr}.

\end{constraints}

Note that the possibility of a {\tt DISTRIBUTE} directive of the form
                                                                        \ICODE
!HPF$ DISTRIBUTE dist-attribute-stuff :: distributee-list
                                                                        \EDOC
is covered by syntax rule \ref{combined-directive-rule} for a
{\it combined-directive}.


Examples:
                                                                        \CODE
!HPF$ DISTRIBUTE D1(BLOCK)
!HPF$ DISTRIBUTE (BLOCK,*,BLOCK) ONTO SQUARE:: D2,D3,D4
                                                                        \EDOC

The meanings of the alternatives for {\it dist-format} are given below.

Define the ceiling division function {\tt CD(J,K)~=~(J+K-1)/K} (using
Fortran integer arithmetic with truncation toward zero.)

Define the ceiling remainder function {\tt CR(J,K)~=~J-K*CD(J,K)}.

The dimensions of a processor arrangement appearing as a {\it
dist-target} are said to {\it correspond} in left-to-right order with
those dimensions of a {\it distributee} for which the corresponding
{\it dist-format} is not {\tt *}.  In the example above, processor
arrangement {\tt SQUARE} must be two-dimensional; its first dimension
corresponds to the first dimensions of {\tt D2}, {\tt D3}, and {\tt D4}
and its second dimension corresponds to the third dimensions of {\tt
D2}, {\tt D3}, and {\tt D4}.

Let \(d\) be the size of a {\it distributee} in a certain dimension and
let \(p\) be the size of the processor arrangement in the corresponding
dimension.  For simplicity, assume all dimensions have a lower bound of
1.  Then {\tt BLOCK(\(m\))} means that a {\it distributee} position
whose index along that dimension is \(j\) is mapped to an abstract
processor whose index along the corresponding dimension of the
processor arrangement is {\tt CD(\(j\),\(m\))} (note that \(m \times p
\geq d\) must be true), and is position number {\tt
\(m\)+CR(\(j\),\(m\))} among positions mapped to that abstract
processor.  The first {\it distributee} position in abstract processor
\(k\) along that axis is position number {\tt 1+\(m\)*(\(k\)-1)}.

The block size \(m\) must be a positive integer.


{\tt BLOCK} by definition means the same as {\tt
BLOCK(CD(\(d\),\(p\)))}.

{\tt CYCLIC(\(m\))} means that a {\it distributee} position whose index
along that dimension is \(j\) is mapped to an abstract processor whose
index along the corresponding dimension of the processor arrangement is
{\tt 1+MODULO(CD(\(j\),\(m\))-1,\(p\))}.  The first {\it distributee}
position in abstract processor \(k\) along that axis is position number
{\tt 1+\(m\)*(\(k\)-1)}.

The block size \(m\) must be a positive integer.


{\tt CYCLIC} by definition means the same as {\tt CYCLIC(1)}.

{\tt CYCLIC(\(m\))} and {\tt BLOCK(\(m\))} imply the same distribution
when \( m \times p \geq d \), but {\tt BLOCK(\(m\))} additionally
asserts that the distribution will not wrap around in a cyclic manner,
which a compiler cannot determine at compile time if \(m\) is not
constant.  Note that {\tt CYCLIC} and {\tt BLOCK} (without argument
expressions) do not imply the same distribution unless \( p \geq d \),
a degenerate case in which the block size is 1 and the distribution
does not wrap around.

Suppose that we have 16 abstract processors and an array of length 100:
                                                                        \CODE
!HPF$ PROCESSORS SEDECIM(16)
      REAL CENTURY(100)
                                                                        \EDOC
Distributing the array {\tt BLOCK} (which in this case would mean
the same as {\tt BLOCK(7)}):
                                                                        \CODE
!HPF$ DISTRIBUTE CENTURY(BLOCK) ONTO SEDECIM
                                                                        \EDOC
results in this mapping of array elements onto abstract processors:
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Distributing the array {\tt BLOCK(8)}:
                                                                        \CODE
!HPF$ DISTRIBUTE CENTURY(BLOCK(8)) ONTO SEDECIM
                                                                        \EDOC
results in this mapping of array elements onto abstract processors:
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Distributing the array {\tt BLOCK(6)} is not HPF-conforming because
\(6 \times 16 < 100\).

Distributing the array {\tt CYCLIC} (which means exactly
the same as {\tt CYCLIC(1)}):
                                                                        \CODE
!HPF$ DISTRIBUTE CENTURY(CYCLIC) ONTO SEDECIM
                                                                        \EDOC
results in this mapping of array elements onto abstract processors:
\begin{center}
\setlength{\unitlength}{0.01in}
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Distributing the array {\tt CYCLIC(3)}:
                                                                        \CODE
!HPF$ DISTRIBUTE CENTURY(CYCLIC(3)) ONTO SEDECIM
                                                                        \EDOC
results in this mapping of array elements onto abstract processors:
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Note that it is perfectly permissible for an array to be distributed so
that some processors have no elements.  Indeed, an array may be ``distributed''
so that all elements reside on one processor.  For example,
                                                                        \CODE
!HPF$ DISTRIBUTE CENTURY(BLOCK(256)) ONTO SEDECIM
                                                                        \EDOC
results in having only one non-empty block---a partially-filled one at that,
having only 100 elements---on processor 1, with processors 2 through 16
having no elements of the array.



A {\tt DISTRIBUTE} directive must not cause
any data object associated with the {\it distributee} via storage association
({\tt COMMON} or {\tt EQUIVALENCE}) to be mapped such that storage
units of a scalar data object are split across more than one abstract processor.
See Section \ref{sequence} for further discussion of storage association.


The statement form of a {\tt DISTRIBUTE} 
directive
may be considered an abbreviation for an attributed form that
happens to mention only one {\it distributee}; for example,
                                                                        \ICODE
!HPF$ DISTRIBUTE distributee ( dist-format-list ) ONTO dist-target
                                                                        \EDOC
is equivalent to
                                                                        \ICODE
!HPF$ DISTRIBUTE ( dist-format-list ) ONTO dist-target :: distributee
                                                                        \EDOC
Note that, to prevent syntactic ambiguity,
the {\it dist-format-clause} must be present in the statement
form, so in general the statement form of the directive may not be
used to specify the mapping of scalars.

If the {\it dist-format-clause} is omitted from the attributed form,
then the language processor may make an arbitrary choice of distribution
formats for each template or array.  So the directive
                                                                        \CODE
!HPF$ DISTRIBUTE ONTO P :: D1,D2,D3
                                                                        \EDOC
means the same as
                                                                        \CODE
!HPF$ DISTRIBUTE ONTO P :: D1
!HPF$ DISTRIBUTE ONTO P :: D2
!HPF$ DISTRIBUTE ONTO P :: D3
                                                                        \EDOC
to which a compiler, perhaps taking into account patterns of use of
{\tt D1}, {\tt D2}, and {\tt D3} within the code, might choose
to supply three distinct distributions such as, for example,
                                                                        \CODE
!HPF$ DISTRIBUTE D1(BLOCK, BLOCK) ONTO P
!HPF$ DISTRIBUTE D2(CYCLIC, BLOCK) ONTO P
!HPF$ DISTRIBUTE D3(BLOCK(43),CYCLIC) ONTO P
                                                                        \EDOC
Then again, the compiler might happen to choose the same
distribution for all three arrays.

In either the statement form or the attributed form,
if the {\tt ONTO} clause is present, it specifies the processor arrangement
that is the target of the distribution.
If the {\tt ONTO}  clause is omitted, then a implementation-dependent
processor arrangement is chosen arbitrarily for each {\it distributee}.
So, for example,
                                                                        \CODE
      REAL, DIMENSION(1000) :: ARTHUR, ARNOLD, LINUS, LUCY
!HPF$ PROCESSORS EXCALIBUR(32)
!HPF$ DISTRIBUTE (BLOCK) ONTO EXCALIBUR :: ARTHUR, ARNOLD
!HPF$ DISTRIBUTE (BLOCK) :: LINUS, LUCY
                                                                        \EDOC
causes the arrays {\tt ARTHUR} and {\tt ARNOLD} to have the same mapping,
so that corresponding elements reside in the same abstract processor,
because they are the same size and distributed in the same way ({\tt BLOCK})
onto the same processor arrangement ({\tt EXCALIBUR}).
However, {\tt LUCY} and {\tt LINUS} do not necessarily have the same
mapping because they might, depending on the implementation,
be distributed onto differently chosen processor arrangements;
so corresponding elements of {\tt LUCY} and {\tt LINUS} might not
reside on the same abstract processor.  (The {\tt ALIGN} directive provides
a way to ensure that two arrays have the same mapping without having
to specify an explicit processor arrangement.)

In a given environment, for some distributions, there may be no 
appropriate processor arrangement.

\section{ALIGN Directive}
\label{ALIGN-SECTION}

The {\tt ALIGN} directive is used to specify that certain data objects
are to be mapped in the same way as certain other data objects.
Operations between aligned data objects are likely to be more efficient
than operations between data objects that are not known to be aligned
(because two objects that are aligned are intended to be mapped to the
same abstract processor).  The {\tt ALIGN} directive is designed to
make it particularly easy to specify explicit mappings for all the
elements of an array at once.  While objects can be aligned in some
cases through careful use of matching {\tt DISTRIBUTE} directives, {\tt
ALIGN} is more general and frequently more convenient.


The {\tt ALIGN} directive may appear only in the {\it
specification-part} of a scoping unit
and can contain only a {\it specification-expr} as a
{\it subscript} or in a {\it subscript-triplet}.

Formally, the syntax of {\tt ALIGN} 
is as follows:

                                                                        \BNF
align-directive            \IS  ALIGN alignee align-directive-stuff

align-directive-stuff      \IS  ( align-source-list ) align-with-clause

align-attribute-stuff      \IS  [ ( align-source-list ) ] align-with-clause

alignee                    \IS  object-name

align-source               \IS  :
                           \OR  *
                           \OR  align-dummy

align-dummy                \IS  scalar-int-variable
                                                                        \FNB
\begin{constraints}
\item An {\it object-name} mentioned as an {\it alignee}
must be a simple name and not a subobject designator.

\item An {\it object-name} mentioned as an {\it alignee} may not
appear as a {\it distributee}.

\item An {\it object-name} mentioned as an {\it alignee} may not
have the {\tt POINTER} attribute.

\item  If the {\it alignee} is scalar,
the {\it align-source-list} (and its surrounding parentheses)
must not appear.  In this case
the statement form of the directive is not allowed.



\item If the {\it align-source-list} is present, its length must equal the
rank of the alignee.

\item An {\it align-dummy} must be a named variable.

\item An object may not have both the {\tt INHERIT} attribute and
the {\tt ALIGN} attribute.  
\end{constraints}

Note that the possibility of an {\tt ALIGN} directive of the form
                                                                        \ICODE
!HPF$ ALIGN align-attribute-stuff :: alignee-list
                                                                        \EDOC
is covered by syntax rule \ref{combined-directive-rule} for a
{\it combined-directive}.

The statement form of an {\tt ALIGN} 
directive
may be considered an abbreviation of an attributed form that
happens to mention only one {\it alignee}:
                                                                        \ICODE
!HPF$ ALIGN alignee ( align-source-list ) WITH align-spec
                                                                        \EDOC
is equivalent to
                                                                        \ICODE
!HPF$ ALIGN ( align-source-list ) WITH align-spec :: alignee
                                                                        \EDOC

If the {\it align-source-list} is omitted from the attributed form and
the {\it  alignee}s are not scalar, the {\it align-source-list} is
assumed to consist of a parenthesized list of ``{\tt :}'' entries,
equal in number to the rank of the {\it alignees}.  Similarly, if the
{\it align-subscript-list} is omitted from the {\it align-spec} in
either form, it is assumed to consist of a parenthesized list of ``{\tt
:}'' entries, equal in number to the rank of the {\it align-target}.
So the directive

                                                                        \CODE
!HPF$ ALIGN WITH B :: A1, A2, A3
                                                                        \EDOC
means
                                                                        \CODE
!HPF$ ALIGN (:,:) WITH B(:,:) :: A1, A2, A3
                                                                        \EDOC
which in turn means the same as
                                                                        \CODE
!HPF$ ALIGN A1(:,:) WITH B(:,:)
!HPF$ ALIGN A2(:,:) WITH B(:,:)
!HPF$ ALIGN A3(:,:) WITH B(:,:)
                                                                        \EDOC

\noindent
because an attributed-form directive that mentions more than one {\it alignee}
is equivalent to a series of identical directives, one for each {\it alignee};
all {\it  alignee}s must have the
same rank.  With this understanding, we will assume below, for the
sake of simplifying the description, that an {\tt ALIGN}
directive has a single {\it alignee}.

Each {\it align-source} corresponds to one axis of the {\it alignee}, and is
specified as either ``{\tt :}'' or ``{\tt *}'' or a dummy variable:

\begin{itemize}

\item
If it is ``{\tt :}'', then positions along that axis will be spread out
across the matching axis of the {\it align-spec} (see below).

\item
If it is ``{\tt *}'', then that axis is {\it collapsed}: positions along
that axis make no difference in determining the corresponding
position within the {\it align-target}.  (Replacing the ``{\tt *}'' with
a dummy variable name not used anywhere else in the directive would
have the same effect; ``{\tt *}'' is merely a convenience that saves the
trouble of inventing a variable name and makes it clear that no
dependence on that dimension is intended.)

\item
A dummy variable is considered to range over all valid
index values for that dimension of the {\it alignee}.

\end{itemize}

The {\tt WITH} clause of an {\tt ALIGN} has the following syntax:
                                                                        \BNF
align-with-clause          \IS  WITH align-spec

align-spec                 \IS  align-target [ ( align-subscript-list ) ]
                           \OR  * align-target [ ( align-subscript-list ) ]

align-target               \IS  object-name
                           \OR  template-name

align-subscript            \IS  int-expr
                           \OR  align-subscript-use
                           \OR  subscript-triplet
                           \OR  *

align-subscript-use    \IS  [ [ int-level-two-expr ] add-op ] align-add-operand
                           \OR  align-subscript-use add-op int-add-operand

align-add-operand          \IS  [ int-add-operand * ] align-primary
                           \OR  align-add-operand * int-mult-operand

align-primary              \IS  align-dummy
                           \OR  ( align-subscript-use )

int-add-operand            \IS  add-operand

int-mult-operand           \IS  mult-operand 

int-level-two-expr           \IS  level-2-expr
                                                                        \FNB

The full syntax is given here for completeness, however some of the
forms will only be discussed in Chapter~\ref{ch-mapping-subr}.  These
``interprocedural'' forms are:
\begin{itemize}
\item The second option of  rule~\ref{align-spec-rule} (containing
the {\tt *} form)
\end{itemize}

\begin{constraints}


\item An {\it object-name} mentioned as an {\it align-target}
must be a simple name and not a subobject designator.

\item An {\it align-target} may not have the {\tt OPTIONAL} attribute.

\item If the {\it align-spec} in an {\tt ALIGN} directive begins with
``{\tt *}'' then every {\it alignee} must be a dummy argument.

\item  Each {\it align-dummy} may appear at most once in an
{\it align-subscript-list}.

\item  An {\it align-subscript-use} expression may contain at most one
occurrence of an {\it align-dummy}.

\item  An {\it align-dummy} may not appear anywhere in the {\it
align-spec} except where explicitly permitted to appear by virtue of
the grammar shown above.  Paraphrased, one may construct an {\it
align-subscript-use} by starting with an {\it align-dummy} and then
doing additive and multiplicative things to it with any integer
expressions that contain no {\it align-dummy}.

\item A {\it subscript} in an {\it align-subscript} may not contain
occurrences of any {\it align-dummy}.

\item An {\it int-add-operand}, {\it int-mult-operand}, or {\it
int-level-two-expr} must be of type integer.

\end{constraints}

The syntax rules for an {\it align-subscript-use} take account of
operator precedence issues, but the basic idea is simple: an {\it
align-subscript-use} is intended to be a linear function of a single
occurrence of an {\it align-dummy}.

For example, the following {\it align-subscript-use} expressions
are valid, assuming that {\tt J}, {\tt K}, and {\tt M}
are {\it align-dummy}s and {\tt N} is not an {\it align-dummy}:

\begin{flushleft}\tt
\begin{tabular}{l@{\quad}l@{\quad}l@{\quad}l@{\quad}l@{\quad}l}
J   &  J+1      &  3-K    &  2*M    &  N*M        &  100-3*M    \\
-J  &  +J       &  -K+3   &  M+2**3 &  M+N    &  -(4*7+IOR(6,9))*K-(13-5/3) \\
M*2 &  N*(M-N)  & 2*(J+1) &  5-K+3  &  10000-M*3  &  2*(3*(K-1)+13)-100
\end{tabular}
\end{flushleft}

The following expressions are not valid {\it align-subscript-use} expressions:
\begin{flushleft}\tt
\begin{tabular}{l@{\quad}l@{\quad}l@{\quad}l@{\quad}l@{\quad}l}
J+J  &  J-J      &  3*K-2*K   &  M*(N-M)  &  2*J-3*J+J & 2*(3*(K-1)+13)-K \\
J*J  &  J+K      &  3/K       &  2**M     &  M*K       &  K-3*M    \\
K-J  &  IOR(J,1) &  -K/3      &  M*(2+M)  &  M*(M-N)   &  2**(2*J-3*J+J)
\end{tabular}
\end{flushleft}

The {\it align-spec} must contain exactly as many {\it subscript-triplets}
as the number of colons (``{\tt :}'') appearing in the {\it align-source-list}.
These are matched up in corresponding left-to-right order, ignoring,
for this purpose, any {\it align-source} that is not a colon and
any {\it align-subscript} that is not a {\it subscript-triplet}.
Consider a dimension of the {\it alignee} for which a colon appears as
an {\it align-source} and
let the lower and upper bounds of that array be {\it LA} and {\it UA}.
Let the corresponding subscript triplet be
{\it LT\/}:{\it UT\/}:{\it ST} or its equivalent.
Then the colon could be replaced by a new, as-yet-unused
dummy variable, say {\tt J}, and the subscript triplet by the expression
{\tt (J-{\it LA})*{\it ST}+{\it LT}}
without affecting the meaning of the directive.  Moreover, the axes
must conform, which means that
\[ \max(0,UA-LA+1) \ = \  \max(0,\lceil (UT-LT+1) / ST \rceil) \]
must be true. (This is entirely analogous to the treatment of array
assignment.)

To simplify the remainder of the discussion,
we assume that every colon in the {\it align-source-list}
has been replaced by new dummy variables
in exactly the fashion just described,
and that every ``{\tt *}'' in the {\it align-source-list}
has likewise been replaced by an otherwise unused dummy variable.
For example,
                                                                        \CODE
!HPF$ ALIGN A(:,*,K,:,:,*) WITH B(31:,:,K+3,20:100:3)
                                                                        \EDOC
may be transformed into its equivalent
                                                                        \CODE
!HPF$ ALIGN A(I,J,K,L,M,N) WITH B(I-LBOUND(A,1)+31,       &
!HPF$            L-LBOUND(A,4)+LBOUND(B,2),K+3,(M-LBOUND(A,5))*3+20)
                                                                        \EDOC
with the attached requirements
\begin{center}
{\tt SIZE(A,1)~.EQ.~UBOUND(B,1)-30}     \\
{\tt SIZE(A,4)~.EQ.~SIZE(B,2)}          \\
{\tt SIZE(A,5)~.EQ.~(100-20+3)/3}
\end{center}
Thus we need consider further only the case where every {\it align-source}
is a dummy variable and no {\it align-subscript} is a {\it subscript-triplet}.

Each dummy variable is considered to range over all valid
index values for the corresponding dimension of the {\it alignee}.
Every combination of possible values for the index variables selects
an element of the {\it alignee}.
The {\it align-spec} indicates a corresponding element (or section) of
the {\it align-target} with which that element of the {\it alignee} should be
aligned; this indication may be a function of the index values, but
the nature of this function is syntactically restricted (as discussed above)
to linear functions
in order to limit the complexity of the implementation.
Each {\it align-dummy} variable may appear at
most once in the {\it align-spec} and only in certain rigidly prescribed
contexts.  The result is that each
{\it align-subscript} expression may contain at most one {\it align-dummy}
variable and the expression is constrained to be a linear function of that
variable.  (Therefore skew alignments are not possible.)

An asterisk ``{\tt *}'' as an {\it align-subscript}
indicates a replicated representation.  Each element of the {\it alignee}
is aligned with every position along that axis of the {\it align-target}.

\begin{rationale}
It may seem strange to use ``{\tt *}'' to mean both collapsing and
replication; the rationale is that ``{\tt *}'' always stands conceptually
for a dummy variable that appears
nowhere else in the statement and ranges over the set of indices for
the indicated dimension. Thus, for example,
                                                                        \CODE
!HPF$ ALIGN A(:) WITH D(:,*)
                                                                        \EDOC
means that a copy of {\tt A} is aligned with every column of {\tt D}, because
it is conceptually equivalent to
                                                                        \ICODE
      for every legitimate index j, align A(:) with D(:,j)
                                                                        \EDOC
just as
                                                                        \CODE
!HPF$ ALIGN A(:,*) WITH D(:)
                                                                        \EDOC
is conceptually equivalent to
                                                                        \ICODE
      for every legitimate index j, align A(:,j) with D(:)
                                                                        \EDOC
Note, however, that while HPF syntax allows
                                                                        \CODE
!HPF$ ALIGN A(:,*) WITH D(:)
                                                                        \EDOC
to be written in the alternate form
                                                                        \CODE
!HPF$ ALIGN A(:,J) WITH D(:)
                                                                        \EDOC
it does {\it not} allow
                                                                        \CODE
!HPF$ ALIGN A(:) WITH D(:,*)
                                                                        \EDOC
to be written in the alternate form
                                                                        \CODE
!HPF$ ALIGN A(:) WITH D(:,J)
                                                                        \EDOC
because that has another meaning (only a variable appearing
in the {\it align-source-list}
following the {\it alignee} is understood to be an {\it align-dummy},
so the current value of the variable {\tt J} is used, thus aligning
{\tt A} with a single column of {\tt D}).

Replication allows an optimizing compiler to arrange to read
whichever copy is closest.  (Of course, when a replicated data object
is written, all copies must be updated, not just one copy.  Replicated
representations are very useful for use as small lookup
tables, where it is much faster to have a copy in each physical
processor but without giving it an extra
dimension that is logically unnecessary to the algorithm.
\end{rationale}

By applying the transformations given above, all cases of an {\it
align-subscript} may be conceptually reduced to either an {\it
int-expr} (not involving an {\it align-dummy}) or an {\it
align-subscript-use} and the {\it align-source-list} may be reduced to
a list of index variables with no ``{\tt *}'' or ``{\tt:}''.  An {\it
align-subscript-list} may then be evaluated for any specific
combination of values for the {\it align-dummy} variables simply by
evaluating each {\it align-subscript} as an expression.  The resulting
subscript values must be legitimate subscripts for the {\it
align-target}.  (This implies that the {\it alignee} is not allowed to
``wrap around'' or ``extend past the edges'' of an {\it align-target}.)
The selected element of the {\it alignee} is then considered to be
aligned with the indicated element of the {\it align-target};  more
precisely, the selected element of the {\it alignee} is considered to
be ultimately aligned with the same object with which the indicated
element of the {\it align-target} is currently ultimately aligned
(possibly itself).

More examples of {\tt ALIGN} directives:
                                                                        \CODE
      INTEGER D1(N)
      LOGICAL D2(N,N)
      REAL, DIMENSION(N,N):: X,A,B,C,AR1,AR2A,P,Q,R,S
!HPF$ ALIGN X(:,*) WITH D1(:)
!HPF$ ALIGN (:,*) WITH D1:: A,B,C,AR1,AR2A
!HPF$ ALIGN WITH D2, DYNAMIC:: P,Q,R,S
                                                                        \EDOC
Note that, in a {\it alignee-list}, the alignees must all have the same
rank but need not all have the same shape; the extents need match only
for dimensions that correspond to colons in the {\it align-source-list}.
This turns out to be an extremely important convenience;
one of the most common cases in current practice is aligning arrays that
match in distributed (``parallel'') dimensions but may differ in
collapsed (``on-processor'') dimensions:
                                                                        \CODE

      REAL A(3,N), B(4,N), C(43,N), Q(N)
!HPF$ DISTRIBUTE Q(BLOCK)
!HPF$ ALIGN (*,:) WITH Q:: A,B,C
                                                                        \EDOC
Here there are processors (perhaps {\tt N} of
them) and arrays of different sizes (3, 4, 43) within each
processor are required.  As far as HPF is concerned,
 the numbers 3, 4, and 43 may be different,
because those axes will be collapsed.  Thus array elements with
indices differing only along that axis will all be aligned with the
same element of {\tt Q} (and thus be specified as residing in the same
processor).

In the following examples, each directive in the group means
the same thing, assuming that corresponding axis upper and lower bounds match:
                                                                        \CODE
!Second axis of X is collapsed
!HPF$ ALIGN X(:,*) WITH D1(:)
!HPF$ ALIGN X(J,*) WITH D1(J)
!HPF$ ALIGN X(J,K) WITH D1(J)

!Replicated representation along second axis of D3
!HPF$ ALIGN X(:,:) WITH D3(:,*,:)
!HPF$ ALIGN X(J,K) WITH D3(J,*,K)

!Transposing two axes
!HPF$ ALIGN X(J,K) WITH D2(K,J)
!HPF$ ALIGN X(J,:) WITH D2(:,J)
!HPF$ ALIGN X(:,K) WITH D2(K,:)
!But there isn't any way to get rid of *both* index variables;
! the subscript-triplet syntax alone cannot express transposition..

!Reversing both axes
!HPF$ ALIGN X(J,K) WITH D2(M-J+1,N-K+1)
!HPF$ ALIGN X(:,:) WITH D2(M:1:-1,N:1:-1)

!Simple case
!HPF$ ALIGN X(J,K) WITH D2(J,K)
!HPF$ ALIGN X(:,:) WITH D2(:,:)
!HPF$ ALIGN (J,K) WITH D2(J,K):: X
!HPF$ ALIGN (:,:) WITH D2(:,:):: X
!HPF$ ALIGN WITH D2:: X
                                                                        \EDOC


\section{Allocatable Arrays and Pointers}
\label{ALLOCATABLE-SECTION}

A variable with the {\tt ALLOCATABLE} attribute may appear
as an {\it alignee}
in an {\tt ALIGN} directive or as a {\it distributee} in a {\tt DISTRIBUTE}
directive.  Such directives do not take effect immediately, however; they
take effect each time the array is allocated by an {\tt ALLOCATE} statement,
rather than on entry to the scoping unit.
The values of all specification expressions in such a directive
are determined once on entry to the scoping unit
and may be used multiple times (or not at all).
For example:
                                                                        \CODE
      SUBROUTINE MILLARD_FILLMORE(N,M)
      REAL, ALLOCATABLE, DIMENSION(:) :: A, B
!HPF$ ALIGN B(I) WITH A(I+N)
!HPF$ DISTRIBUTE A(BLOCK(M*2))
      N = 43
      M = 91
      ALLOCATE(A(27))
      ALLOCATE(B(13))
      ...
                                                                        \EDOC
The values of the expressions {\tt N} and {\tt M*2}
on entry to the subprogram are conceptually retained by the
{\tt ALIGN} and {\tt DISTRIBUTE} directives for later use at allocation time.
When the array {\tt A} is allocated, it is distributed with a block size
equal to the retained value of {\tt M*2}, not the value 182.
When the array {\tt B} is allocated, it is aligned relative to {\tt A}
according to the retained value of {\tt N}, not its new value 43.

Note that it would have been incorrect in the {\tt MILLARD_FILLMORE} example
to perform the two {\tt ALLOCATE} statements in the opposite order.
In general, when an object {\tt X} is created it may be aligned to another
object {\tt Y} only if {\tt Y} has already been created or allocated.
The following example illustrates several related cases.
                                                                        \CODE
      SUBROUTINE WARREN_HARDING(P,Q)
      REAL P(:)
      REAL Q(:)
      REAL R(SIZE(Q))
      REAL, ALLOCATABLE :: S(:),T(:)
!HPF$ ALIGN P(I) WITH T(I)                        !Nonconforming
!HPF$ ALIGN Q(I) WITH *T(I)                       !Nonconforming
!HPF$ ALIGN R(I) WITH T(I)                        !Nonconforming
!HPF$ ALIGN S(I) WITH T(I)
      ALLOCATE(S(SIZE(Q)))                        !Nonconforming
      ALLOCATE(T(SIZE(Q)))
                                                                        \EDOC
The {\tt ALIGN} directives are not HPF-conforming because the array {\tt T}
has not yet been allocated at the time that the various alignments
must take place.  The four cases differ slightly in their details.
The arrays {\tt P} and {\tt Q} already exist on entry to the
subroutine, but because {\tt T} is not yet allocated, one cannot
correctly prescribe the alignment of {\tt P} or describe the
alignment of {\tt Q} relative to {\tt T}.  (See Chapter~\ref{ch-mapping-subr}
for a discussion of prescriptive and descriptive directives.)
The array {\tt R} is created on subroutine entry and its size
can correctly depend on the {\tt SIZE} of {\tt Q}, but the alignment
of {\tt R} cannot be specified in terms of the alignment of {\tt T}
any more than its size can be specified in terms of the size of {\tt T}.
It {\it is} permitted to have an alignment directive for {\tt S}
in terms of {\tt T}, because the alignment action does not take place
until {\tt S} is allocated; however, the first {\tt ALLOCATE}
statement is nonconforming because {\tt S} needs to be aligned
but at that point in time {\tt T} is still unallocated.


When an array is allocated, it will be aligned to an existing template
if there is an explicit {\tt ALIGN} directive for the allocatable
variable.  If there is no explicit {\tt ALIGN} directive, then the array
will be ultimately aligned with itself.  It is forbidden for any
other object to be ultimately aligned to an array at the time the
array becomes undefined by reason of deallocation.  All this applies
regardless of whether the name originally used in the {\tt ALLOCATE}
statement when the array was created had the {\tt ALLOCATABLE} attribute or
the {\tt POINTER} attribute.

Pointers cannot be explicitly mapped in HPF and thus
can only be associated with objects which are not explicitly mapped.
When used for allocation, the compiler may
choose any arbitrary mapping for data allocated through the pointer.
Explicit mapping of pointers is allowed under the approved extensions - see
Section~\ref{POINTERS-SECTION} for details.
Also, the the relationship of pointers and sequence attributes is
described in Section~\ref{sequence}. 


\section{PROCESSORS Directive}
\label{PROCESSORS-SECTION}

The {\tt PROCESSORS} directive declares one or more rectilinear
processor arrangements, specifying for each one its name, its rank
(number of dimensions), and the extent in each dimension.  It may
appear only in the {\it specification-part} of a scoping unit.  Every
dimension of a processor arrangement must have nonzero extent;
therefore a processor arrangement cannot be empty.

In the language of section 14.1.2 of the Fortran standard, processor
arrangements are local entities of class (1); therefore a processor
arrangement may not have the same name as a variable, named constant,
internal procedure, etc., in the same scoping unit.  Names of processor
arrangements obey the same rules for host and use association as other
names in the long list in section 12.1.2.2.1 of the Fortran
standard.


A processor arrangement declared in a module has the default accessibility
of the module.

\begin{rationale}
Because the name of a processor arrangement is not a first-class entity
in HPF, but must appear only in directives, it cannot appear in an
{\it access-stmt} ({\tt PRIVATE} or {\tt PUBLIC}).
If directives ever become full-fledged Fortran statements rather
than structured comments, then it would be appropriate to allow
the accessibility of a processor arrangement to be controlled
by listing its name in an {\it access-stmt}.
\end{rationale}


If two processor arrangements have the same shape, then corresponding
elements of the two arrangements are understood to refer to the same
abstract processor.  (It is anticipated that
implementation-dependent directives provided by some HPF
implementations could overrule the default correspondence of processor
arrangements that have the same shape.)

If directives collectively specify that two objects be mapped to the
same abstract processor at a given instant during the program
execution, the intent is that the two objects be mapped to the same
physical processor at that instant.

The intrinsic functions {\tt NUMBER_OF_PROCESSORS} and {\tt
PROCESSORS_SHAPE} may be used to inquire about the total number of
actual physical processors used to execute the program.  This
information may then be used to calculate appropriate sizes for the
declared abstract processor arrangements.

                                                                        \BNF
processors-directive       \IS  PROCESSORS processors-decl-list

processors-decl            \IS  processors-name [ ( explicit-shape-spec-list ) ]
                                                                        \FNB


Examples:

                                                                        \CODE
!HPF$ PROCESSORS P(N)
!HPF$ PROCESSORS Q(NUMBER_OF_PROCESSORS()),       &
!HPF$            R(8,NUMBER_OF_PROCESSORS()/8)
!HPF$ PROCESSORS BIZARRO(1972:1997,-20:17)
!HPF$ PROCESSORS SCALARPROC
                                                                        \EDOC

\noindent
If no shape is specified, then the declared processor arrangement is
conceptually scalar.

\begin{rationale}
A scalar processor arrangement may be useful as a way of
indicating that certain scalar data should be kept together but need
not interact strongly with distributed data.  Depending on the
implementation architecture, data distributed onto such a processor
arrangement may reside in a single ``control'' or ``host'' processor
(if the machine has one), or may reside in an arbitrarily chosen
processor, or may be replicated over all processors.  For target
architectures that have a set of computational processors and a
separate scalar host computer, a natural implementation is to map
every scalar processor arrangement onto the host processor.  For
target architectures that have a set of computational processors but
no separate scalar ``host'' computer, data mapped to a scalar
processor arrangement might be mapped to some arbitrarily chosen
computational processor or replicated onto all computational
processors.
\end{rationale}

An HPF compiler is required to accept any
{\tt PROCESSORS} declaration in which the product of the extents of each
declared processor arrangement is equal to the number of physical
processors that would be returned by the call {\tt NUMBER_OF_PROCESSORS()}.
It must also accept all declarations of scalar {\tt PROCESSOR}
arrangements.  Other cases may be handled as well, depending on the
implementation.

For compatibility with the Fortran attribute syntax, an optional
``{\tt ::}'' may be inserted.  The shape may also be specified with the
{\tt DIMENSION} attribute:
                                                                        \CODE
!HPF$ PROCESSORS :: RUBIK(3,3,3)
!HPF$ PROCESSORS, DIMENSION(3,3,3) :: RUBIK
                                                                        \EDOC
As in Fortran, an {\it explicit-shape-spec-list} in a {\it processors-decl}
will override an explicit {\tt DIMENSION} attribute:
                                                                        \CODE
!HPF$ PROCESSORS, DIMENSION(3,3,3) ::      &
!HPF$            RUBIK, RUBIKS_REVENGE(4,4,4), SOMA
                                                                        \EDOC
Here {\tt RUBIKS_REVENGE} is \( 4 \times 4 \times 4 \) while
{\tt RUBIK} and {\tt SOMA} are each \( 3 \times 3 \times 3 \).
(By the rules enunciated above, however, such a statement
may not be completely portable because no HPF language processor is
required to handle shapes of total sizes 27 and 64 simultaneously.)

Returning from a subprogram causes all processor arrangements
declared local to that subprogram to become undefined.  It is
not HPF-conforming for any array or template to be distributed onto a processor
arrangement at the time the processor arrangement becomes undefined
unless at least one of two conditions holds:

\begin{itemize}

\item The array or template itself becomes undefined at the same time
by virtue of returning from the subprogram.

\item Whenever the subprogram is called, the processor arrangement
is always locally defined in the same way, with identical lower bounds,
and identical upper bounds.

\begin{rationale}
Note that the second condition is slightly less stringent than requiring
all expressions to be constant.  This allows calls to
{\tt NUMBER_OF_PROCESSORS} or {\tt PROCESSORS_SHAPE} to appear
without violating the condition.
\end{rationale}

\end{itemize}

Variables in {\tt COMMON} or having the {\tt SAVE} attribute may be
mapped to a locally declared processor arrangement, but because the
first condition cannot hold for such variables (they don't become
undefined), the second condition must be observed.
This allows {\tt COMMON} variables to work properly through the customary
strategy of putting identical declarations in each scoping unit that
needs to use them, while allowing the processor arrangements to which
they may be mapped to depend on the value returned
by {\tt NUMBER_OF_PROCESSORS}. (See Section~\ref{sequence} for
further information on mapping common variables.)

\begin{implementors}
It may be desirable to have a way for the user to specify at compile
time the number of physical processors on which the program is to be
executed.  This might be specified either by a implementation-dependent
directive, for example, or through the programming environment (for
example, as a UNIX command-line argument).  Such facilities are
beyond the scope of the HPF specification, but as food for thought we
offer the following illustrative hypothetical examples:
                                                                        \CODE
!Declaration for multiprocessor by ABC Corporation
!ABC$ PHYSICAL PROCESSORS(8)
!Declaration for mpp by XYZ Incorporated
!XYZ$ PHYSICAL PROCESSORS(65536)
!Declaration for hypercube machine by PDQ Limited
!PDQ$ PHYSICAL PROCESSORS(2,2,2,2,2,2,2,2,2,2)
!Declaration for two-dimensional grid machine by TLA GmbH
!TLA$ PHYSICAL PROCESSORS(128,64)
!One of the preceding might affect the following
!HPF$ PROCESSORS P(NUMBER_OF_PROCESSORS())
                                                                        \EDOC

It may furthermore be desirable to have a way for the user to specify
the precise mapping of the processor arrangement declared in a
{\tt PROCESSORS} statement to the physical processors of the executing
hardware.  Again, this might be specified either by a
implementation-dependent directive or through the programming
environment (for example, as a UNIX command-line argument); 
such facilities are beyond the scope of the HPF specification, but as
food for thought we offer the following illustrative hypothetical
example:
                                                                        \CODE
!PDQ$ PHYSICAL PROCESSORS(2,2,2,2,2,2,2,2,2,2,2,2,2)
!HPF$ PROCESSORS G(8,64,16)
!PDQ$ MACHINE LAYOUT G(:GRAY(0:2),:GRAY(6:11),:BINARY(3:5,12))
                                                                        \EDOC
This might specify that the first dimension of {\tt G} should use hypercube
axes 0, 1, 2 with a Gray-code ordering; the second dimension should
use hypercube axes 6 through 11 with a Gray-code ordering; and the
third dimension should use hypercube axes 3, 4, 5, and 12 with a
binary ordering.
\end{implementors}




\section{TEMPLATE Directive}
\label{TEMPLATE-SECTION}

The {\tt TEMPLATE} directive declares one or more templates, specifying for
each the name, the rank (number of dimensions), and the extent in each
dimension.  It must appear in the {\it specification-part} of a scoping unit.

In the language of section 14.1.2 of the Fortran standard,
templates are local entities of class (1); therefore a template may
not have the same name as a variable, named constant, internal
procedure, etc., in the same scoping unit.  Template names obey the
rules for host and use association as other names in the
list in section 12.1.2.2.1 of the Fortran standard.


A template declared in a module has the default accessibility
of the module.

\begin{rationale}
Because the name of a template is not a first-class entity
in HPF, but must appear only in directives, it cannot appear in an
{\it access-stmt} ({\tt PRIVATE} or {\tt PUBLIC}).
If directives ever become full-fledged Fortran statements rather
than structured comments, then it would be appropriate to allow
the accessibility of a template to be controlled
by listing its name in an {\it access-stmt}.
\end{rationale}



A template is simply an abstract space of indexed positions; it can
be considered as an ``array of nothings'' (as compared to an ``array of
integers,'' say).
%%%If an array is a cat, then a template is a Cheshire
%%%cat, and the index space is the grin.
A template may be used as an abstract {\it align-target} that may
then be distributed.
                                                                        \BNF
template-directive             \IS  TEMPLATE template-decl-list

template-decl              \IS  template-name [ ( explicit-shape-spec-list ) ]

                                                                        \FNB

Examples:
                                                                        \CODE
!HPF$ TEMPLATE A(N)
!HPF$ TEMPLATE B(N,N), C(N,2*N)
!HPF$ TEMPLATE DOPEY(100,100),SNEEZY(24),GRUMPY(17,3,5)
                                                                        \EDOC

If the ``{\tt ::}'' syntax is used, then the declared templates may optionally
be distributed in the same {\it combined-directive}.  In this case
all templates declared by the
directive must have the same rank so that the {\tt DISTRIBUTE} attribute
will be meaningful.  The {\tt DIMENSION} attribute may also be used.
                                                                        \CODE
!HPF$ TEMPLATE, DISTRIBUTE(BLOCK,*) ::    &
!HPF$                              WHINEY(64,64),MOPEY(128,128)
!HPF$ TEMPLATE, DIMENSION(91,91) :: BORED,WHEEZY,PERKY
                                                                        \EDOC

Templates are useful in the particular situation where one must align
several arrays relative to one another but there is no need to
declare a single array that spans the entire index space of interest.
For example, one might want four \( N \times N \) arrays aligned to the four
corners of a template of size \( (N+1) \times (N+1) \): 
                                                                        \CODE
!HPF$ TEMPLATE, DISTRIBUTE(BLOCK, BLOCK) :: EARTH(N+1,N+1)
      REAL, DIMENSION(N,N) :: NW, NE, SW, SE
!HPF$ ALIGN NW(I,J) WITH EARTH( I , J )
!HPF$ ALIGN NE(I,J) WITH EARTH( I ,J+1)
!HPF$ ALIGN SW(I,J) WITH EARTH(I+1, J )
!HPF$ ALIGN SE(I,J) WITH EARTH(I+1,J+1)
                                                                        \EDOC
Templates may also be useful in making assertions about the mapping of
dummy arguments (see Chapter~\ref{ch-mapping-subr}).

Unlike arrays, templates cannot be in {\tt COMMON}.  So two templates
declared in different scoping units will always be distinct, even if
they are given the same name.  The only way for two program units to
refer to the same template is to declare the template in a module that
is then used by the two program units.

Templates are not passed through the subprogram argument interface.
The template to which a dummy argument is aligned is always distinct
from the template to which the actual argument is aligned, though it
may be a copy (see Section \ref{INHERIT-SECTION}).  On exit from a
subprogram, an HPF implementation arranges that the actual argument is
aligned with the same template with which it was aligned before the
call.

Returning from a subprogram causes all templates declared local to that
subprogram to become undefined.  It is not HPF-conforming for any
variable to be aligned to a template at the time the template becomes
undefined unless at least one of two conditions holds:

\begin{itemize}

\item The variable itself becomes undefined at the same time by virtue
of returning from the subprogram.

\item Whenever the subprogram is called, the template is always locally
defined in the same way, with identical lower bounds, identical upper
bounds, and identical distribution information (if any) onto
identically defined processor arrangements (see Section
\ref{PROCESSORS-SECTION}).

\begin{rationale}
Note that this second condition is slightly less stringent than
requiring all expressions to be constant.  This allows calls to {\tt
NUMBER_OF_PROCESSORS} or {\tt PROCESSORS_SHAPE} to appear without
violating the condition.
\end{rationale}

\end{itemize}

\noindent
Variables in {\tt COMMON} or having the {\tt SAVE} attribute may be
mapped to a locally declared template, but because the first condition
cannot hold for such variable (they don't become undefined), the second
condition must be observed.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Material from the old chapter 7
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Storage and Sequence Association}
\label{sequence}

HPF allows the mapping of
data objects across multiple processors in order to improve 
parallel performance.  Fortran specifies
relationships between the storage for data objects associated 
through {\tt COMMON} and {\tt EQUIVALENCE} statements, and the order of 
array elements during association at procedure boundaries
between actual arguments and dummy arguments.
Otherwise, the location of data is not constrained by the
language.

{\tt COMMON} and {\tt EQUIVALENCE} statements constrain the alignment
of different data items based on the underlying model
of storage units and storage sequences:

\begin{quotation}
{\em Storage association is the association of two or more
data objects that occurs when two or more storage sequences 
share or are aligned with one or more storage units.}

--- Fortran Standard (14.6.3.1)

\end{quotation}
The model of storage association is a single linearly 
addressed memory, based on the traditional single address 
space, single memory unit architecture. This model can cause 
severe inefficiencies on architectures where storage for 
data objects is mapped.

Sequence association refers to the order of array elements 
that Fortran requires when an array expression or array 
element is associated with a dummy array argument:

\begin{quotation}
{\em The rank and shape of the actual argument need not agree 
with the rank and shape of the dummy argument, \ldots}

--- Fortran Standard (12.4.1.4)

\end{quotation}
As with storage association, sequence association
is a natural concept only in systems with
a linearly addressed memory.

As an aid to porting FORTRAN 77 codes, HPF allows codes that 
rely on sequence and storage association to be valid in HPF.
Some modification to existing FORTRAN 77 codes may 
nevertheless be necessary.
This section explains the relationship between HPF data 
mapping and sequence and storage association.

\subsection{Storage Association}

\subsubsection{Definitions}

\label{sequence-defs}

\begin{enumerate}

\item {\tt COMMON} blocks are either {\it sequential}
or {\it nonsequential}, as determined by either explicit 
directive or compiler default.  A sequential {\tt COMMON} block 
has a single common  block storage sequence (Fortran Standard 5.5.2.1).

\item An {\it aggregate variable group}
is a collection of variables whose individual storage
sequences are parts of a single storage sequence.

Variables associated by {\tt EQUIVALENCE} statements
or by a combination of {\tt EQUIVALENCE} and {\tt COMMON} statements
form an aggregate variable group. The variables of a
sequential {\tt COMMON} block form a single aggregate variable
group.


\item The {\it size} of an aggregate variable group is the 
number of storage units in the group's storage sequence 
(Fortran Standard 14.6.3.1).

\item  \label{seq-var} Data objects are either
{\it sequential} or {\it nonsequential}.
A data object is {\it sequential} if and only if any of the
following holds:


\begin{enumerate}

\item it appears in a sequential {\tt COMMON} block;

\item it is a member of an aggregate variable group;

\item it is an assumed-size array;

\item it is a component of a derived type with
the Fortran {\tt SEQUENCE} attribute; or

\item it is declared to be sequential in an HPF {\tt SEQUENCE} 
directive.

\end{enumerate}

A sequential object can be storage associated or
sequence associated;  nonsequential objects cannot.

\item A {\tt COMMON} block contains a sequence of {\it components}.
Each component is either an aggregate
variable group, or a variable that is not a member of any
aggregate variable group.
Sequential {\tt COMMON} blocks contain a single component.
Nonsequential {\tt COMMON} blocks may
contain several components that  may be
sequential variables or aggregate variable groups or
may be nonsequential.




\end{enumerate}


\subsubsection{Examples of Definitions}

                                                                \CODE
      IMPLICIT REAL (A-Z)
      COMMON /FOO/ A(100), B(100), C(100), D(100), E(100)
      DIMENSION X(100), Y(150), Z(200)


!Example 1:
      EQUIVALENCE ( A(1), Z(1) )
!Four components: (A, B), C, D, E
!Sizes are: 200, 100, 100, 100

!Example 2:
      EQUIVALENCE ( A(51), X(1) ) ( B(100), Y(1) )
!Two components (A, B, C, D), E
!Sizes are: 400, 100

!Example 3:
!HPF$ SEQUENCE /FOO/
!The COMMON has one component, (A, B, C, D, E) 
!Size is 500
                                                                \EDOC
\noindent
The {\tt COMMON} block {\tt /FOO/} is nonsequential
in Examples 1 and 2.
Aggregate variable groups are shown as components in 
parentheses.  

\subsection {Sequence Directive}

A {\tt SEQUENCE} directive is defined to allow a user to declare 
explicitly that data objects or {\tt COMMON}  blocks are to be treated 
by the compiler as sequential.  ({\tt COMMON} blocks are by default 
nonsequential.  Data objects are
nonsequential unless Definition~\ref{seq-var} applies.) 
Some implementations may supply an  optional compilation 
environment where the {\tt SEQUENCE} directive is applied by
default.  For completeness in such an environment, HPF 
defines a {\tt NO SEQUENCE} directive to allow a user to 
establish that the usual
nonsequential default should apply to a scoping unit, or selected
data objects and {\tt COMMON} blocks within the scoping unit.

                                        \BNF
sequence-directive  \IS    SEQUENCE [ [ :: ] association-name-list ]
                    \OR NO SEQUENCE [ [ :: ] association-name-list ]

association-name        \IS object-name
                        \OR / [ common-block-name ]  /
                                        \FNB

\begin{constraints}

\item An object name or {\tt COMMON} block name may appear at most once
in a {\it sequence-directive} within any scoping unit.


\item Only one sequence directive with no {\it association-name-list}
is permitted in the same scoping unit.


\end{constraints}

A pointer declared with the {\tt SEQUENCE} attribute can be only be
associated with sequential objects.

\subsubsection {Storage Association Rules}

\begin{enumerate}

\item A {\it sequence-directive} with an empty {\it
association-name-list}  is treated as if it contained the name of all
implicitly mapped objects and {\tt COMMON} blocks in the scoping unit
which cannot otherwise be determined to be sequential or nonsequential
by their language context.

\item A sequential object may not be explicitly mapped.

\item No explicit mapping may be given for a component of a derived
type having the Fortran {\tt SEQUENCE} attribute. 
Note
that this rule is applicable only under the approved extensions
since components of derived types cannot be explicitly mapped in HPF.

\item No explicit mapping may be given for a dummy argument that
is an assumed size array.


\item If a {\tt COMMON} block is nonsequential, then all of the
following must hold:

\begin{enumerate}

\item Every occurrence of the {\tt COMMON}  block has exactly the 
same number of components with each corresponding component 
having a storage sequence of exactly the same size;

\item If a component is a nonsequential variable in {\it any}
occurrence of the {\tt COMMON} block, then it must be
nonsequential with identical  type, shape, and mapping
attributes in {\it every}  occurrence of the {\tt COMMON} block; and

\item Every occurrence of the {\tt COMMON}  block must be 
nonsequential.

\end{enumerate}

\end{enumerate}


\subsubsection{Storage Association Discussion}
\begin{users}
Under these rules, variables in a {\tt COMMON} block can be mapped 
as long as the components of the {\tt COMMON} block are the same in 
every scoping unit that declares the {\tt COMMON} block. 

Correct Fortran programs will not necessarily
be correct without modification in HPF.
The use of
{\tt EQUIVALENCE} with {\tt COMMON} blocks can impact the
mappability of data
objects in subtle ways. To allow maximum 
optimization for performance, the HPF default for data objects is to 
consider them mappable.
In order to get correct separate compilation for
subprograms that use {\tt COMMON} blocks with different aggregate
variable groups in different scoping units, it will be 
necessary to insert the HPF {\tt SEQUENCE} directive.  

As a check-list 
for a user to determine the status of a data object or {\tt COMMON} block,
the following questions can be applied, in order:


\begin{itemize}

\item Does the object appear in some explicit language context
which dictates that the object be
sequential (e.g. {\tt EQUIVALENCE}) or nonsequential?

\item If not, does the object appear in an explicit mapping
directive?

\item If not, does the object or {\tt COMMON} block name appear in the 
list of names on a {\tt SEQUENCE} or {\tt NO SEQUENCE} directive?

\item If not, does the scoping unit contain a nameless {\tt SEQUENCE}
 or {\tt NO SEQUENCE}?

\item If not, is the compilation affected by some special 
implementation-dependent environment which dictates that names
default to {\tt SEQUENCE}?

\item If not, then the compiler will  consider the object or {\tt COMMON}
block name non-sequential and is free to apply data mapping
optimizations disregarding Fortran sequence and storage association.

\end{itemize}

\end{users}

\begin{implementors}
In order to protect the user and to facilitate portability of 
older codes, two implementation options are strongly 
recommended. First, every implementation should supply some 
mechanism to verify that the type and shape of every mappable 
array and the sizes of aggregate variable groups in  {\tt COMMON} blocks 
are the same in every scoping unit unless the {\tt COMMON}  blocks are  
declared to be sequential. This same check should
also verify that identical mappings have been selected for 
the variables in {\tt COMMON}  blocks.  Implementations without 
interprocedural information can use a link-time check. The 
second implementation option recommended is a  
mechanism to declare that data objects and {\tt COMMON} blocks for
a given compilation should be considered sequential unless 
declared otherwise. The purpose of this feature is to permit 
compilation of large old libraries or  subprograms where 
storage association is known to exist without requiring that 
the code be modified to apply the HPF
{\tt SEQUENCE} directive to every {\tt COMMON} block.
\end{implementors}
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% File: mapping-ext.tex

% Contents:
% Approved Extensions for data mapping for HPF 2.0 document, including
%        GenBlock
%        indirect
%        range
%        shadow
%        subsets
%        derived types
%        more on pointers.

% Revision history:
% May-10-96        Created by Charles Koelbel, Rice University
%                (From HPF 2.0 proposals)
% May-22-96        Modified by Piyush Mehrotra to include all of
%               the above topics
% Aug-8-96         Modified by Piyush Mehrotra:
%               modified subsection on remapping across procedure boundaries
%               modified the section on pointers based on proposals passed
%                       in the July meeting
%               added clarifications and examples to the range section


\chapter{Approved Extensions for Data Mapping}
\label{ch-mapping-ext}


{\em
Comments on this chapter should be directed to 
Piyush Mehrotra ({\tt pm@icase.edu}),
Carl Offner ({\tt offner@hpc.pko.dec.com}),
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Extended Mapping}'' as the {\tt Subject:}
line.
\par
}

This chapter describes a set of data mapping features which extend
the capabilities provided by the base set as described in 
Chapter~\ref{ch-mapping-base}. These extensions can be
divided into two categories. The first set of extensions
provide the user greater control over the mapping of the data. 
These include directives for dynamic remapping of data
which allow the user to redistribute and realign at runtime data which
has been declared {\tt DYNAMIC}.
The {\tt ONTO} clause used in the {\tt DISTRIBUTE} directive is extended
to allow direct distribution to subsets of processors.
Explicit mapping of pointers and components of derived
types are also introduced.
Two new distributions are included, the {\tt GEN\_BLOCK} 
distribution which generalizes the block distribution and
the {\tt INDIRECT} which allows the mapping of individual array
elements to be specified through a mapping array.

The programmer can use the second set of extensions to provide the
compiler with information useful for generating efficient
code. This category includes the range directives which
allows the user to specify the range of distribution that
a dynamically distributed array, a pointer or a formal
argument may have. The shadow directive allows the user
to specify the amount of additional space required on a
processor to accommodate non-local elements in a
nearest-neighbor computation.

Since this chapter deals with extensions, we repeat some of
the sections of Chapter~\ref{ch-mapping-base} and~\ref{ch-mapping-subr} 
providing new rules and extending old
ones where necessary. 
%When extending a rule we use {\tt extended-xx} 
%as the new rule name with the understanding
%that it will replace the old rule name, {\tt xx}, everywhere.



\section{Extended Model}

The fundamental model for allocation of data to abstract
processors still remains a two-level mapping as described in
Chapter~\ref{ch-mapping-base}. However, it is extended to
allow the dynamic remapping of the data objects as
illustrated by the following diagram:

\begin{center}

\setlength{\unitlength}{0.01in}
\begin{picture}(600,240)(0,30)
\thicklines
\put(100,150){\circle{50}}
\put(242,150){\circle{50}}
\put(383,150){\circle{50}}
\put(525,150){\circle{50}}
\put(125,150){\vector(1,0){92}}
\put(267,150){\vector(1,0){91}}
\put(408,150){\vector(1,0){92}}
\put(56,190){\shortstack{Arrays or\strut\\other
objects\strut}}
\put(192,190){\shortstack{Group of\strut\\aligned
objects\strut}}
\put(328,190){\shortstack{Abstract\strut\\processors as
a\strut
                \\user-declared\strut\\Cartesian
mesh\strut}}
\put(494,190){\shortstack{Physical\strut\\processors\strut}}
\put(135,50){\shortstack{{\tt ALIGN}\strut\\(static) or\strut
                \\{\tt REALIGN}\strut\\(dynamic)\strut}}
\put(265,50){\shortstack{{\tt DISTRIBUTE}\strut\\(static) or\strut
                \\{\tt REDISTRIBUTE}\strut\\(dynamic)\strut}}
\put(400,50){\shortstack{Optional\strut\\implementation-\strut
                \\dependent\strut\\directive\strut}}
\end{picture}

\end{center}

Thus, objects can now be remapped at execution time using
the executable directives {\tt REALIGN} and {\tt REDISTRIBUTE}
Any object that is the root of
an alignment tree, i.e., is not explicitly aligned to
another object, can be explicitly redistributed.
Redistributing such an object causes all objects ultimately
aligned with it to be also redistributed so as to maintain the
alignment relationships.

Any object that is not a root
of an alignment tree can be explicitly realigned but not explicitly
redistributed. Such a realignment does not change the
mapping of any other object.
Note that such remapping of data may require communication
among the processors.


By analogy with the Fortran 90 {\tt ALLOCATABLE} attribute, HPF includes
the attribute {\tt DYNAMIC}.  It is not permitted
to {\tt REALIGN} an array that has not been declared {\tt DYNAMIC}.
Similarly, it is not permitted to {\tt REDISTRIBUTE} an array or template
that has not been declared {\tt DYNAMIC}.

Saved local variables, variables in common, and variables accessed by
use association must not be implicitly remapped - e.g., by having
variable distribution formats or being aligned with entities having
variable distribution formats.  Of these three categories of
variables, only variables accessed by use association may have the
{\tt DYNAMIC} attribute.

\section{Syntax of Data Alignment and Distribution Directives}


As in the case of other mapping directives,
the executable directives {\tt REALIGN} and {\tt REDISTRIBUTE}
also come in two forms (statement form and attribute form) but
may not be combined with other attributes in a single directive.
The {\tt RANGE} attribute may be combined with other attributes
in a single directive.

                                                                        \BNF
extended-combined-attribute  \IS  ALIGN align-attribute-stuff
                           \OR  DISTRIBUTE dist-attribute-stuff
                           \OR  DYNAMIC
                           \OR  INHERIT
                           \OR  TEMPLATE
                           \OR  PROCESSORS
                           \OR  DIMENSION ( explicit-shape-spec-list )
                           \OR  RANGE range-attr-stuff-list
                                                                        \FNB


\section{REDISTRIBUTE Directive}
\label{REDISTRIBUTE-SECTION}

The {\tt REDISTRIBUTE} directive is similar to the {\tt DISTRIBUTE}
directive but is considered executable.  An array (or template) may be
redistributed at any time, provided it has been declared {\tt DYNAMIC}
(see Section \ref{DYNAMIC-SECTION}).  Any other arrays currently
ultimately aligned with an array (or template) when it is redistributed
are also remapped to reflect the new distribution, in such a way as to
preserve alignment relationships (see Section \ref{ALIGN-SECTION}).
(This can require a lot of computational and communication effort at
run time; the programmer must take care when using this feature.)

The {\tt DISTRIBUTE} directive may appear only in the {\it specification-part}
of a scoping unit.  The {\tt REDISTRIBUTE} directive may appear
only in the {\it execution-part} of a scoping unit.  The principal
difference between {\tt DISTRIBUTE} and {\tt REDISTRIBUTE} is
that {\tt DISTRIBUTE} must contain only a {\it specification-expr} as the
argument to a 
distribution format, e.g.,
{\tt BLOCK} or {\tt CYCLIC}, whereas in {\tt REDISTRIBUTE}
such an argument may be any integer expression.  Another difference is that
{\tt DISTRIBUTE} is an attribute, and so can be combined with other attributes
as part of a {\it combined-directive}, whereas {\tt REDISTRIBUTE} is not an attribute
(although a {\tt REDISTRIBUTE} statement may be written in the
style of attributed syntax, using ``{\tt ::}'' punctuation).

Formally, the syntax of the {\tt DISTRIBUTE} and
{\tt REDISTRIBUTE} directives is:

                                                                        \BNF
redistribute-directive     \IS  REDISTRIBUTE distributee dist-directive-stuff
                   \OR  REDISTRIBUTE dist-attribute-stuff :: distributee-list
                                                                        \FNB
\begin{constraints}

\item  A {\it distributee} that appears in a {\tt REDISTRIBUTE} directive
must have the {\tt DYNAMIC} attribute (see Section \ref{DYNAMIC-SECTION}).

\item Neither the {\it dist-format-clause} nor the {\it dist-target}
in a {\tt REDISTRIBUTE} may begin with ``{\tt *}''.

\end{constraints}

If a range directive (see Section~\ref{range}) has been used to restrict
the set of distribution formats allowed for a {\it distributee}, then 
the new mapping should match one of the formats specified in the range 
directive.

A {\tt REDISTRIBUTE} directive must not cause any data object
associated with the {\it distributee} via storage association ({\tt
COMMON} or {\tt EQUIVALENCE}) to be mapped such that storage units of
a scalar data object are split across more than one abstract
processor.  See Section \ref{sequence} for further discussion of
storage association.


The statement form of a {\tt REDISTRIBUTE} directive
may be considered an abbreviation for an attributed form that
happens to mention only one {\it distributee}; for example,
                                                                        \CODE
!HPF$ REDISTRIBUTE distributee ( dist-format-list ) ONTO dist-target
                                                                        \EDOC
is equivalent to
                                                                        \CODE
!HPF$ REDISTRIBUTE ( dist-format-list ) ONTO dist-target :: distributee
                                                                        \EDOC

\section{REALIGN Directive}
\label{REALIGN-SECTION}

The {\tt REALIGN} directive is similar to the {\tt ALIGN} directive but
is considered executable.  An array (or template) may be realigned at
any time, provided it has been declared {\tt DYNAMIC} (see Section
\ref{DYNAMIC-SECTION}) Unlike redistribution (see Section
\ref{DISTRIBUTE-SECTION}), realigning a data object does not cause any
other object to be remapped.  (However, realignment of even a single
object, if it is large, could require a lot of computational and
communication effort at run time; the programmer must take care when
using this feature.)

The {\tt ALIGN} directive may appear only in the {\it
specification-part} of a scoping unit.  The {\tt REALIGN} directive is
similar but may appear only in the {\it execution-part} of a scoping
unit.  The principal difference between {\tt ALIGN} and {\tt REALIGN}
is that {\tt ALIGN} must contain only a {\it specification-expr} as a
{\it subscript} or in a {\it subscript-triplet}, whereas in {\tt
REALIGN} such subscripts may be any integer expressions.  Another
difference is that {\tt ALIGN} is an attribute, and so can be combined
with other attributes as part of a {\it combined-directive}, whereas
{\tt REALIGN} is not an attribute (although a {\tt REALIGN} statement
may be written in the style of attributed syntax, using ``{\tt ::}''
punctuation).

Formally, the syntax of {\tt REALIGN} is as follows:

                                                                        \BNF
realign-directive          \IS  REALIGN alignee align-directive-stuff
                           \OR  REALIGN align-attribute-stuff :: alignee-list
                                                                        \FNB
\begin{constraints}

\item  Any {\it alignee} that appears in a {\tt REALIGN} directive
must have the {\tt DYNAMIC} attribute (see Section \ref{DYNAMIC-SECTION}).


\item If the {\tt align-target} specified in the {\tt align-with-clause}
has the {\tt DYNAMIC} attribute, then each {\tt alignee} must also have the
{\tt DYNAMIC} attribute.

\item An object may not have both the {\tt INHERIT} attribute and
the {\tt ALIGN} attribute.  (However, an object with the {\tt INHERIT}
attribute may appear as an {\it alignee} in a {\tt REALIGN} directive,
provided that it does not appear as a {\it distributee} in a {\tt DISTRIBUTE}
or {\tt REDISTRIBUTE} directive.)
\end{constraints}

If a range directive (see Section~\ref{range}) has been used to restrict
the set of distribution formats allowed for an {\it alignee}, then 
the new mapping should match one of the formats specified in the range 
directive.

\section{DYNAMIC Directive}
\label{DYNAMIC-SECTION}

The {\tt DYNAMIC} attribute specifies that an object may be dynamically
realigned or redistributed.
                                                                        \BNF
dynamic-directive      \IS  DYNAMIC  alignee-or-distributee-list

alignee-or-distributee \IS  alignee
                       \OR  distributee
                                                                        \FNB

\begin{constraints}

\item An object in {\tt COMMON} may not be declared {\tt DYNAMIC} and
may not be aligned to an object (or template) that is {\tt DYNAMIC}.
(To get this kind of effect,  Fortran 90 modules must be used instead
of {\tt COMMON} blocks.)

\item An object with the {\tt SAVE} attribute may not be declared {\tt DYNAMIC}
and may not be aligned to an object (or template) that is {\tt DYNAMIC}.

\end{constraints}

A {\tt REALIGN} directive may not be applied to an {\it alignee} that does not
have the {\tt DYNAMIC} attribute.  A {\tt REDISTRIBUTE} directive may not be
applied to a {\it distributee} that does not have the {\tt DYNAMIC} attribute.

A {\tt DYNAMIC} directive may be combined with other directives, with the
attributes stated in any order, consistent with the Fortran
90 attribute syntax.

Examples:
                                                                        \CODE
!HPF$ DYNAMIC A,B,C,D,E
!HPF$ DYNAMIC:: A,B,C,D,E
!HPF$ DYNAMIC, ALIGN WITH SNEEZY:: X,Y,Z
!HPF$ ALIGN WITH SNEEZY, DYNAMIC:: X,Y,Z
!HPF$ DYNAMIC, DISTRIBUTE(BLOCK, BLOCK) :: X,Y
!HPF$ DISTRIBUTE(BLOCK, BLOCK), DYNAMIC :: X,Y
                                                                        \EDOC
The first two examples mean exactly the same thing.
The next two examples mean exactly the same second thing.
The last two examples mean exactly the same third thing.

The three directives
                                                                        \CODE
!HPF$ TEMPLATE A(64,64),B(64,64),C(64,64),D(64,64)
!HPF$ DISTRIBUTE(BLOCK, BLOCK) ONTO P:: A,B,C,D
!HPF$ DYNAMIC A,B,C,D
                                                                        \EDOC
may be combined into a single directive as follows:
                                                                        \CODE
!HPF$ TEMPLATE, DISTRIBUTE(BLOCK, BLOCK) ONTO P,   &
!HPF$   DIMENSION(64,64),DYNAMIC :: A,B,C,D
                                                                        \EDOC


An {\tt ALLOCATABLE} object may also be given the {\tt DYNAMIC} attribute.
If an {\tt ALLOCATE} statement is immediately followed by {\tt REDISTRIBUTE}
and/or {\tt REALIGN} directives,
the meaning in principle is that the array is first created
with the statically declared mapping, if any, then immediately remapped.
In practice there is an obvious optimization: create the array
in the processors to which it is about to be remapped, in a single
step.  HPF implementors are strongly encouraged to implement this
optimization and HPF programmers are encouraged to rely upon it.
Here is an example:
                                                                       \CODE
      REAL,ALLOCATABLE(:,:) :: TINKER, EVERS
!HPF$ DYNAMIC :: TINKER, EVERS
      REAL, ALLOCATABLE :: CHANCE(:)
!HPF$ DISTRIBUTE(BLOCK),DYNAMIC :: CHANCE
      ...
      READ 6,M,N
      ALLOCATE(TINKER(N*M,N*M))
!HPF$ REDISTRIBUTE TINKER(CYCLIC, BLOCK)
      ALLOCATE(EVERS(N,N))
!HPF$ REALIGN EVERS(:,:) WITH TINKER(M::M,1::M)
      ALLOCATE(CHANCE(10000))
!HPF$ REDISTRIBUTE CHANCE(CYCLIC)
                                                                       \EDOC
While {\tt CHANCE} is by default always allocated with a {\tt BLOCK}
distribution, it should be possible for a compiler to notice that it will
immediately be remapped to a {\tt CYCLIC} distribution.  Similar remarks
apply to {\tt TINKER} and {\tt EVERS}.  (Note that {\tt EVERS}
is mapped in a thinly-spread-out manner onto {\tt TINKER};
adjacent elements of {\tt EVERS} are mapped to elements of
{\tt TINKER} separated by a stride {\tt M}.  This thinly-spread-out
mapping is put in the lower left corner of {\tt TINKER},
because {\tt EVERS(1,1)} is mapped to {\tt TINKER(M,1)}.)



\section{Remapping and Subprogram Interfaces}
\label{DYNAMIC-DUMMY-SECTION}

The rules on the interaction of the {\tt REALIGN} and {\tt
REDISTRIBUTE} directives with a subprogram argument interface are:
\begin{enumerate}

\item A dummy argument may be declared {\tt DYNAMIC}.  However, it is subject
to the general restrictions concerning the use of the name of an
array to stand for its associated template.

The effect of any redistribution of the dummy after the procedure returns
to the caller is dependent on the attribute of the actual argument.
If the actual argument associated with the dummy has also been declared 
{\tt DYNAMIC}, then any explicit remapping of the dummy is visible in the
caller after the procedure returns.
If a range directive (see Section~\ref{range}) has been used to restrict
the set of distribution formats allowed for 
the actual argument, then 
the new mapping should match one of the formats specified in the range 
directive.

If the actual argument associated with the dummy has not been declared 
{\tt DYNAMIC} then the original mapping of the actual has to be restored
on return. 
When the subprogram returns
and the caller resumes execution, all objects accessible to the caller
after the call which are not declared
{\tt DYNAMIC},  are mapped exactly as they were before the call.


\item If an array or any section thereof is accessible by two or more
paths, it is not HPF-conforming to remap it through any of those paths.  For
example, if an array is passed as an actual argument, it is forbidden
to realign that array, or to redistribute an array or template to which
it was aligned at the time of the call, until the subprogram has
returned from the call.  This prevents nasty aliasing problems.  An
example:

                                                                        \CODE
      MODULE FOO
      REAL A(10,10)
!HPF$ DYNAMIC ::  A
      END

      PROGRAM MAIN
      USE FOO
      CALL SUB(A(1:5,3:9))
      END

      SUBROUTINE SUB(B)
      USE FOO
      REAL B(:,:)
!HPF$ DYNAMIC ::  B
      ...
!HPF$ REDISTRIBUTE A            !Nonconforming
      ...
      END
                                                                        \EDOC
Situations such as this are forbidden, for the same reasons that an assignment
to {\tt A} at the statement marked ``Nonconforming'' would also be forbidden.
In general, in {\it any} situation where assignment to a variable
would be nonconforming by reason of aliasing, remapping of that variable
by an explicit {\tt REALIGN} or {\tt REDISTRIBUTE} directive is also forbidden.

Note that it is legal to remap a host-associated or use-associated variable
in a subprogram if it has been declared {\tt DYNAMIC} and is accessible
only through a single path. Such remappings stay in effect even after
the subprogram has returned to its caller.

\end{enumerate}



%----------------------------------------------------------------------------
% Mapping to subsets proposal
%--------------------------------------------------------------------------
\section{Mapping to Processor Subsets}
\label{mapping-proc-subset}

This extension allows  objects  to  be  directly  distributed  to  processor
subsets  by allowing a processor subset to be specified
where  a  processor  could  be  named,  e.g.,  in  a   {\tt DISTRIBUTE}
directive.   The  specified subset must be a proper subset of the
named processor arrangement.

Formally the syntax of the extended {\it dist-target} is as
follows:

                                                                        \BNF
extended-dist-target    \IS processor-name [( section-subscript-list )]
                        \OR * processor-name [( section-subscript-list )]
                        \OR *
                                                                        \FNB
\begin{constraints}

\item The {\it section-subscript}s in the
{\it section-subscript-list} may not be 
{\it vector-subscript}s and are restricted to
either {\it subscript}s or {\it subscript-triplet}s.

\item In the {\it section-subscript-list}, 
the number of {\it section-subscript}s
must equal the rank of the {\it processor-name}.

\end{constraints}
            


                                                                        \CODE
!Example 1
!HPF$ PROCESSORS P(10)
        REAL A(100)
!HPF$ DISTRIBUTE A(BLOCK) ONTO P(2:5)


!Example 2
!HPF$ PROCESSORS Q(10,10)
        REAL A(100,100)
!HPF$ DISTRIBUTE B(BLOCK,BLOCK) ONTO Q(5:10,5:10)
                                                                        \EDOC

In Example 1, the array A is distributed by block across the
processors P(2) to P(5) while in the second example, the array B
is distributed across the lower right quadrant of the processor array Q.

\begin{users}
This extension is most useful in conjunction with the
tasking construct, see Section~\ref{tasking}, which allows
multiple independent phases of a computation to execute simultaneously
on different subsets of processors. A similar situation arises when 
the code uses multiple data structures which can be computed in 
parallel where the computation on each individual object also
exhibits parallelism, e.g., the multiple blocks in
a multi-block grid used in some fluid dynamics calculation. Here, the
individual blocks have to be distributed over subsets of processors
to exploit both levels of parallelism.
\end{users}


\section{Pointers}
\label{POINTERS-SECTION}


Under the approved extensions, pointers can be explicitly mapped.
Formally, this implies that the constraints that a {\it distributee}
and an {\it alignee} may not have the {\tt POINTER} attribute
as stated in 
Sections~\ref{DISTRIBUTE-SECTION} and~\ref{ALIGN-SECTION} respectively,
have to be removed.

As in the case of an allocatable object, the mapping specification
for a pointer does not take effect immediately but plays a role when
the pointer becomes pointer associated with a target either through allocation
or through pointer assignment.

When a pointer with an explicit mapping is used in an {\tt ALLOCATE}
statement, the data is allocated with the specified mapping.


For example:
                                                                        \CODE
      REAL, POINTER, DIMENSION(:) :: A, B
!HPF$ ALIGN B WITH A
!HPF$ DISTRIBUTE A(BLOCK)
      ...
      ALLOCATE(A(100))
      ALLOCATE(B(50))
      ...
      ALLOCATE(B(200))                  ! Nonconforming
                                                                        \EDOC

Pointer {\it A}  is declared to have a {\tt BLOCK}
distribution while pointer {\tt B} is declared to be identically
aligned with {\it A}. When {\it A} is allocated, it is created
with a block distribution.
When {\it B} is allocated, it is aligned with the first 50 elements
of {\it A}. Note, that the allocation statements
may not occur in the opposite
order, since an object may be aligned to another only if
it has already been  created or allocated.
Also, the second allocation for {\it B} is nonconforming,
since a larger object, {\it B} here, cannot be aligned
with a smaller object, {\it A} in this case.

A pointer with an explicit mapping can be pointer
associated with a target through a pointer assignment statement
under the following constraints:
\begin{enumerate}

\item The target must have an explicit mapping.

\item The target may not be a section of an array. 

\item The distribution of each dimension of the ultimate
align target of the pointer, as specified by the
explicit mapping, must match with the distribution of corresponding
dimension of the ultimate align target of the pointer target.
\end{enumerate}

For example:
                                                                        \CODE
      REAL, POINTER, DIMENSION(:,:) :: A
!HPF$ DISTRIBUTE A(BLOCK,BLOCK) 
      REAL, TARGET, DIMENSION (100, 100) ::  B, C, D
!HPF$ DISTRIBUTE B(BLOCK, BLOCK)
!HPF$ DISTRIBUTE C(CYCLIC, BLOCK)
      ...
      A => B                 ! Conforming
      A => B(1:50, 1:50)     ! Nonconforming: target must be  a whole array.
      A => C                 ! Nonconforming: the distribution in the 
                             ! second dimension does not match
      A => D                 ! Nonconforming: D is not explicitly mapped
      ...
                                                                        \EDOC


If a pointer has a partially specified (or underspecified)
mapping, it can be
pointer associated with a target as long as inheriting the rest
of the mapping from the target provides a complete specification
which is compatible with the mapping of the target.
For example, the following pointer assignment is valid even though
no processor arrangement is specified for the pointer:
                                                                        \CODE
      REAL, POINTER, DIMENSION(:) :: A
      REAL, TARGET, DIMENSION(100) ::  B
!HPF$ DISTRIBUTE A(BLOCK)
!HPF$ DISTRIBUTE (BLOCK) ONTO P :: B
      ...
      A => B                 ! Conforming
      ...
                                                                        \EDOC

\subsection{Transcriptive Mapping for Pointers}

In order to allow pointers to point to targets with any explicit mappings
and also to sections of arrays,
we allow the transcriptive mapping to be used for local pointer variables
also.

For example:
                                                                        \CODE
      REAL, POINTER, DIMENSION(:) :: A
!HPF$ DISTRIBUTE * :: A
      REAL, TARGET, DIMENSION(100) ::  B, C
!HPF$ DISTRIBUTE B(BLOCK), C(CYCLIC)
      ...
      A => B                 ! Conforming
      A => C                 ! Conforming
      A => C(1:50)           ! Conforming
      ...
                                                                        \EDOC

Here, the {\tt *} is used to indicate a transcriptive distribution for the
pointer {\it A} and thus it can be pointer associated with both
targets {\it B} and {\it C} distributed by {\tt BLOCK}
and {\tt CYCLIC} respectively.

To allow pointers to have a transcriptive distribution, we have
to change the constraint for {\it dist-format-clause} as specified
in Section~\ref{DISTRIBUTE-SECTION}, to read as follows:

\begin{constraints}
\item If either the {\it dist-format-clause} or the {\it dist-target}
in a {\tt DISTRIBUTE} directive begins with ``{\tt *}'' 
then every {\it distributee} must be a dummy argument, 
{\em 
except if the {\em distributee}
has the {\tt POINTER} attribute.}
\end{constraints}

Note that pointers with the transcriptive distribution
can be pointer associated only with targets which
have explicit mappings.
When such pointers are used in an {\tt ALLOCATE} statement,
the compiler may choose any arbitrary mapping for the allocated data.

A range declaration (see Section~\ref{range}) can be used to restrict
the set of distribution formats.

\subsection{Pointers with the DYNAMIC Attribute}
A pointer with an explicit mapping, as described above, may
also have the {\tt DYNAMIC} attribute. Such pointers can be
pointer associated with targets
if and only if they have the {\tt DYNAMIC} attribute.
In such a case,
the target associated with the pointer may be remapped
using a {\tt REDISTRIBUTE} or {\tt REALIGN} statement under the
following restrictions.

A pointer may be used in {\tt REALIGN} and {\tt REDISTRIBUTE} as an
{\it alignee}, {\it align-target}, or {\it distributee}
if and only if it is currently
associated with a whole array, not an array section.  One may remap an object
by using a pointer as an {\it alignee} or {\it distributee} only if the
object was created by {\tt ALLOCATE} but is not an {\tt ALLOCATABLE} array.

Note that when an object is remapped, the new mapping is
visible through any pointer that may be associated with the object.

%The following has been deleted based on proposal approved in
%the July 96 meeting. If this is to be retained it should also
% be moved to the section on remappings.
%Any directive that remaps an object constitutes an assertion on the
%part of the programmer that the remainder of program execution would
%be unaffected if all pointers associated with any portion of the
%object were instantly to acquire undefined pointer association
%status, except for the one pointer, if any, used to indicate the
%object in the remapping directive.

%\begin{implementors}
%If HPF directives were ever to be absorbed as actual Fortran
%statements, the previous paragraph could be written as
%``Remapping an object causes all pointers associated with any portion
%of the object to have undefined pointer association status, except
%for the one pointer, if any, used to indicate the object in the
%remapping directive.''  The more complicated wording here is intended
%to avoid any implication that the remapping directives, in the form
%of structured comment annotations, have any effect on the execution
%semantics, as opposed to the execution speed, of the annotated
%program.
%\end{implementors}

\subsection{Pointers and Subprograms}


If a dummy pointer argument is not explicitly mapped, then the
actual pointer argument must not also be explicitly mapped.

If a dummy pointer argument has an explicit prescriptive or
descriptive mapping then the actual argument must follow
the rules for pointer assignment as stated above.
That is, the actual argument must be explicitly mapped,
must point to a whole object, and the distributions of
the corresponding dimensions  of the ultimate align targets of the
actual and formal arguments must match.

If a dummy pointer argument has a transcriptive mapping
then the actual argument must be explicitly mapped.
The dummy argument in this case assumes the distribution
of the actual.
Again a range declaration (see Section~\ref{range}) can be used to restrict
the set of distribution formats of the actual.

{\em Alternative proposal:
If a dummy pointer argument has a transcriptive mapping
any actual pointer argument is allowed including one
that is not explicitly mapped.
The dummy argument in this case assumes the distribution
of the actual.
Again a range declaration (see Section~\ref{range}) can be used to restrict
the set of distribution formats of the actual.
}

A dummy pointer argument may have the {\tt DYNAMIC} attribute.
In this case, the actual pointer argument must also have the
{\tt DYNAMIC} argument. The target associated with the
dummy argument may be redistributed under the restrictions stated in
the last subsection.
Following Fortran rules, if the actual is also visible
(through host- or use-association), the target may be redistributed
only through the dummy argument.
If the dummy argument is redistributed, then the actual argument has the new 
mapping on return from the procedure. 
In such a case, the new mapping
must match the range restrictions (if any) of the actual.


\section{Mapping of Derived Type Components}
%-----------------------------------------------------------------------------
% Derive type mappings, apparent date Jan 18, 1996
%-----------------------------------------------------------------------------


An {\tt ALIGN}, {\tt DISTRIBUTE}, or {\tt DYNAMIC} directive may appear within a
{\it derived-type-def} wherever a {\it component-def-stmt} may appear.  Every
{\it alignee} or {\it distributee} within such a directive must be the name of
a component defined within that {\it derived-type-def}.
To allow mapping of the structure components, the rules have to be extended 
as follows:


                                                                        \BNF

extended-distributee    \IS  object-name
                        \OR  template-name
                        \OR  structure-component
                                                                        \FNB

A derived type is said to be an {\it explicitly mapped type}
if any of its components is explicitly mapped or if any of its
components is of an explicitly mapped type.

\begin{constraints}
\item A component of a derived type may be explicitly distributed
only if the type of the component is not an explicitly mapped type.

\item A variable or array of a derived type may be explicitly
distributed only if the derived type is not an explicitly mapped type.

\item A {\it distributee} in a {\tt DISTRIBUTE} directive may not be a
{\it structure-component}, only a {\it component-name}.

\item A {\it distributee} that is a {\it structure-component} may occur
only in a {\tt REDISTRIBUTE} directive 
and every {\it part-ref}
except the rightmost must be scalar (rank zero).
The rightmost {\it part-name} 
in the {\it structure-component} must have the {\tt DYNAMIC} attribute.
\end{constraints}



                                                                        \BNF
extended-alignee        \IS  object-name
                        \OR  structure-component
                                                                        \FNB



\begin{constraints}
\item A component of a derived type may be explicitly aligned
only if the type of the component is not an explicitly mapped type.

\item A variable or array of a derived type may be explicitly
aligned only if the derived type is not an explicitly mapped type.

\item An {\it alignee} in an {\tt ALIGN} directive may not be a
{\it structure-component}.

\item An {\it alignee} that is a {\it structure-component} may occur
only in a {\tt REALIGN} directive 
and every {\it part-ref}
except the rightmost must be scalar (rank zero).
The rightmost {\it part-name} in the {\it structure-component} must
have the {\tt DYNAMIC} attribute.

\end{constraints}



The above constraints imply that components of structures can be 
mapped within the derived type definition itself such that
any objects of that type are created with the specified mapping.
Structure components which have been declared {\tt DYNAMIC} may be
remapped using the {\tt REDISTRIBUTE} or {\tt REALIGN} directive.


Example:

                                                                        \CODE
      TYPE SIMPLE
        REAL S(100)
!HPF$   DISTRIBUTE S(BLOCK)
      END TYPE SIMPLE

!HPF$ TEMPLATE, DISTRIBUTE(BLOCK, *) :: HAIRY_TEMPLATE(47,73)

      TYPE COMPLICATED
        INTEGER SIZE
        REAL RV(100,100), KV(100,100), QV(47,73)
! Arrays RV, KV, and QV may be mapped
!HPF$   DISTRIBUTE (BLOCK, BLOCK):: RV, KV
!HPF$   ALIGN WITH HAIRY_TEMPLATE :: QV
        TYPE(SIMPLE) SV(100)
! The following directive is not valid because SIMPLE
!  is an explicitly mapped type.
!HPF$   DISTRIBUTE SV(BLOCK) 
      END TYPE COMPLICATED

      TYPE(COMPLICATED) LOTSOF(20)

! The following directive is not valid because COMPLICATED 
! is an explicitly mapped type.
!HPF$ DISTRIBUTE LOTSOF(BLOCK)
                                                                        \EDOC

Here, a component of the derived type {\tt SIMPLE} has been mapped;
thus objects of this type, e.g., {\tt SV} in type {\tt COMPLICATED},
cannot be distributed. The array {\tt LOTSOF} cannot be distributed for the 
same reason.


Components of structures can be remapped using the {\tt REDISTRIBUTE}
or {\tt REALIGN} directive if they have been declared {\tt DYNAMIC}.
For example, the following code fragment can be used to allocate and map 
multiple blocks (called {\tt SUBGRID} here) of a multi-block grid:

                                                                        \CODE
!HPF$ PROCESSORS P( number_of_processors() )

      TYPE SUBGRID
        INTEGER SIZE
        INTEGER LO, HI          ! target subset of processors
        REAL, POINTER BL(:)
!HPF$   DYNAMIC BL
      END TYPE SUBGRID

      TYPE (SUBGRID), ALLOCATABLE :: GRID(:)

      READ (*,*) SUBGRID_COUNT
      ALLOCATE GRID(SUBGRID_COUNT)
      DO I = 1, SUBGRID_COUNT
        READ(*,*) GRID(I)%SIZE
      END DO

! Compute processor subsets for each subgrid, setting the LO and HI values
      CALL FIGURE_THE_PROCS ( GRID, number_of_processors()) 
! Allocate each subgrid and distribute to the computed processors subset 
      DO I = 1, SUBGRID_COUNT
        ALLOCATE( GRID(I)%BL( GRID(I)%SIZE ) )
!HPF$   REDISTRIBUTE GRID(I)%BL(BLOCK) ONTO P( GRID(I)%LO : GRID(I)%HI )
     END DO
                                                                        \EDOC



%-----------------------------------------------------------------------------
% Indirect mapping proposal, apparent date Jan 18, 1996
%----------------------------------------------------------------------------

\section{New Distribution Formats}
\label{dist-formats}

This section describes two new 
distribution formats. Formally, we can extend the syntax as follows:

                                                                \BNF
extended-dist-format    \IS  BLOCK  [ ( int-expr ) ]
                        \OR  CYCLIC [ ( int-expr ) ]
                        \OR GEN\_BLOCK (int-array)
                        \OR INDIRECT (int-array)
                        \OR  *
                                                                \FNB

\begin{constraints}
\item
    An {\it int-array} appearing in a {\it extended-dist-format} of a
    {\tt DISTRIBUTE} or {\tt REDISTRIBUTE} directive must be an 
integer array of rank 1.

\item
    An {\it int-array} appearing in a {\it extended-dist-format} of a
    {\tt DISTRIBUTE} directive must be a {\it restricted-expr}.

\item
    The size of any 
 {\it int-array} appearing with a {\tt GEN\_BLOCK} distribution must be
equal to the extent of the corresponding dimension of the target processor
arrangement.

\item
    The size of any 
 {\it int-array} appearing with an {\tt INDIRECT} distribution must be
equal to the extent of the corresponding dimension of the {\it distributee}
to which the distribution is to be applied.

\end{constraints}

The ``generalized'' block distribution, {\tt GEN\_BLOCK}, allows
contiguous segments of an array, of possibly unequal sizes, to be mapped
onto processors. The sizes of the segments 
are specified by values of a user-defined integer mapping array,
one value per target processor of the mapping.
That is,  the {\it ith} element of the mapping array specifies the
size of the block to be stored on the {\it ith} processor
of the target processor arrangement.
Thus, the values of the mapping arrays are restricted to be 
non-negative numbers and their sum must be greater than or equal to
the extent of the corresponding dimension the array being distributed.

The mapping array has to be a restricted expression when used in  the
{\tt DISTRIBUTE}   directive,  but  can  be  an  array  variable  in  a
{\tt REDISTRIBUTE} directive. In the latter case, changing the value of
the  map  array  after  the  directive has been executed will not
change the mapping of the distributed array.


Let {\it l} and {\it u} be the lower and upper bounds of the dimension
of the {\it distributee}, {\it MAP} be the mapping array
 and let {\it BS(i):BE(i)} be the resultant 
elements mapped to the {\it ith} processor in the corresponding
dimension of the target processor arrangements.
Then,
\begin{eqnarray*}
BS (1) & = & l,\\
BE (i) & = & max( BS(i)+MAP(i)-1, u),\\
BS (i) & = & BE(i-1) + 1.\\
\end{eqnarray*}

Example:
                                                                        \CODE
        PARAMETER (S = /2,25,20,0,8,65/)
!HPF$ PROCESSORS P(6)
        REAL A(100), B(200), new(6)
!HPF$ DISTRIBUTE A( GEN_BLOCK( S) ) ONTO P
!HPF$ DYNAMIC  B
        ...
       new = ...
!HPF$  REDISTRIBUTE ( B( GEN_BLOCK(new) )
                                                                        \EDOC
Given the above specification, array elements A(1:2) are mapped on P(1),
A(3:27) are mapped on P(2), A(28:37) are mapped on P(3),
no elements are mapped on P(4), A(37:45) are mapped on P(5), and
A(46:100) are mapped on P(6).
The array {\it B} is distributed based on the array {\it new} whose 
values are computed at runtime. 

\begin{implementors}
Accessing elements of an array distributed using the generalized 
block distribution may require accessing the values of the mapping
array at runtime. However, since the size of such an array 
is equal to that of the processor arrangement, it can in most
cases be replicated over all processors.

For dynamic arrays, an independent copy of the mapping array
will have to be maintained internally so that a change
in the values of the mapping array does not affect the access 
of the distributed array.
\end{implementors}



There are many scientific applications in which the structure  of
the  underlying domain is such that it does not map directly onto
Fortran data structures. For example, in many CFD applications  an
unstructured mesh (consisting of triangles in 2D or tetrahedra in
3D) is used to represent the underlying domain. The nodes of such
a mesh are generally represented by a one-dimensional array while
another is used to  represent  their  interconnections.   Mapping
such  arrays  using the structured distribution mechanisms, {\tt BLOCK}
and {\tt CYCLIC}, results in mappings in which unrelated  elements  are
mapped  onto  the  same  processor. This in turn leads to massive
amounts of unnecessary communication.   What  is  required  is  a
mechanism  to  map a related set of arbitrary array elements onto
the same processor.  The  {\tt INDIRECT}  distribution  
provides  such  a  mechanism.  


The  {\tt INDIRECT}  distribution  allows  a  many-to-one  mapping   of
elements  of  a  dimension  of a data array to a dimension of the
target processor arrangement. An integer array is used to specify
the  target  processor  of  each  individual element of the array
dimension being distributed.  That is, the {\it ith} element of the mapping
array  provides  the  processor  number  onto which the {\it ith} array
element is to be mapped.  Since the mapping array maps array elements
onto  processor  elements, the extent of the mapping array must match
the extent of the dimension of the array it is distributing. Also,
the  values of the mapping array must lie between the lower and upper
bound of the target dimension of the processor arrangement.

The mapping array has to be a restricted expression when used in  the
{\tt DISTRIBUTE}   directive,  but  can  be  an  array  variable  in  a
{\tt REDISTRIBUTE} directive. In the latter case, changing the value of
the  mapping  array  after  the  directive has been executed will not
change the mapping of the distributed array.



Example:

                                                                        \CODE
!HPF$ PROCESSORS P(4)
        REAL A(100), B(50)
        INTEGER map1(100), map2(50)
        PARAMETER (map1 = /1,3,4,3,3,2,1,4, ..../)
!HPF$ DYNAMIC B
!HPF$ DISTRIBUTE A( INDIRECT(map1) ) ONTO P
!HPF$ DISTRIBUTE map2(BLOCK) ONTO P

        map2 = ...
!HPF$ DISTRIBUTE B( INDIRECT(map2) ) ONTO P
        ....
                                                                        \EDOC

Here, the array {\it A} is distributed statically using the constant
array {\it map1}.  Thus:

\hspace{0.5in}
\parbox{3in}{
A(1) is mapped onto P(1),\\
A(2) is mapped onto P(3),\\
A(3) is mapped onto P(4),\\
A(4) is mapped onto P(3),\\
A(5) is mapped onto P(3),\\
A(6) is mapped onto P(2),\\
A(7) is mapped onto P(1),\\
A(5) is mapped onto P(4), and so on.\\
}

The array {\it B} is declared  dynamic and is redistributed using
the mapping array {\it map2}.



\begin{implementors}
In general, the {\tt INDIRECT} distribution is going to be used in  the
{\tt REDISTRIBUTE}  directive  with an array variable as the map array.
Also, since the size of the mapping array must be  the  same  as  the
array  being  distributed,  it  will  itself  be distributed most
likely using the {\tt BLOCK} distribution.  This raises several issues.
To  correctly  implement  this  distribution,  the runtime system
should maintain a (distributed) copy of the mapping array so that  if
the  program  modifies  the  mapping array, the distribution does not
change.  Using an array variable as a mapping array implies that  the
location  of  each  element  of the array will not be known until
runtime. Thus, a communication maybe required to figure  out  the
location  of  a  specific array element.
\end{implementors}


%-----------------------------------------------------------------------------
% Shadow regions proposal, apparent date Feb 7, 1996
%-----------------------------------------------------------------------------

\section{Range Directive}
\label{range}

The {\tt RANGE} attribute is used to restrict the possible distribution 
formats for an object or template that has the {\tt DYNAMIC} attribute or 
a transcriptive distribution format (including pointers).


                                                                \BNF
range-directive         \IS RANGE ranger range-attr-stuff-list

ranger                  \IS object-name
                        \OR template-name

range-attr-stuff        \IS ( range-attr-list )

range-attr              \IS range-dist-format
                        \OR ALL

range-dist-format       \IS BLOCK [ ()]
                        \OR  CYCLIC [ () ]
                        \OR GEN\_BLOCK
                        \OR INDIRECT 
                        \OR  *

                                                                \FNB

\begin{constraints}

\item
The {\it ranger} must have the {\tt DYNAMIC} attribute, 
the {\tt INHERIT} attribute and no explicit {\tt DISTRIBUTE},
or it must have been specified with a {\it dist-format-clause}
of {\tt *} in a {\tt DISTRIBUTE} or combined directive.

\item
The length of any {\it range-attr-list} must be equal to the rank of
the {\it ranger}.

\item
The {\it ranger} must not appear as an alignee in an {\tt ALIGN}
or {\tt REALIGN} directive.
\end{constraints}


Since the length of each {\it range-attr-list} is the same as the rank of
the {\it ranger}, each {\it range-attr},
{\it R}, in each {\it range-attr-stuff} corresponds
positionally to a dimension {\it D} of the ranger.  This dimension {\it D} in
turn corresponds (though not necessarily positionally) to an axis {\it A}
of the template with which the ranger is ultimately aligned.

With this notation, a {\tt RANGE} attribute on a {\it ranger} is equivalent to
the following constraint:
\begin{quote}
For at least one {\it range-attr-stuff} in the {\it range-attr-stuff-list},
every {\it range-attr}, {\it R}, must be compatible with the distribution
format of the corresponding axis {\it A}.
\end{quote}

Note, that if there is no corresponding dimension in the ultimate align target,
then a {\tt *} or {\tt ALL} must be used as the {\tt range-attr}.


This compatibility must be maintained by any {\tt DISTRIBUTE}
or {\tt REDISTRIBUTE} directive in which the {\it ranger} appears as
a distributee, or if the ranger has the {\tt POINTER}
attribute and is transcriptively distributed, 
for any target with which the {\it ranger}
becomes associated.

A distribution format of 

\begin{enumerate}

\item
{\tt BLOCK} is compatible with a {\it range-dist-format} of {\tt BLOCK},
{\tt BLOCK()} or {\tt CYCLIC()};

\item
{\tt BLOCK(n)} is compatible with a {\it range-dist-format} of 
{\tt BLOCK()} or {\tt CYCLIC()};

\item
{\tt CYCLIC} is compatible with a {\it range-dist-format} of {\tt CYCLIC}
or {\tt CYCLIC()};

\item
{\tt CYCLIC(n)} is compatible with a {\it range-dist-format} of {\tt CYCLIC()};

\item
{\tt GEN\_BLOCK} is compatible with a {\it range-dist-format} of 
{\tt GEN\_BLOCK};

\item
{\tt INDIRECT} is compatible with a {\it range-dist-format} of {\tt INDIRECT};

\item
{\tt *} is compatible with a {\it range-dist-format} of {\tt *}.


\end{enumerate}

All distribution formats are compatible with a {\it range-dist-format} of 
{\tt ALL}.

Examples:

                                                                \CODE
!HPF$    DISTRIBUTE T(BLOCK)
!HPF$    ALIGN A(I,J) WITH T(I) 

         CALL SUB(A)
            ....

         SUBROUTINE SUB(X)
!HPF$    INHERIT X
!HPF$    RANGE (BLOCK, *),  (CYCLIC, *)
                                                                \EDOC

Since the ultimate align target of X, the inherited template T in this case,
does not have a second dimension, only a {\tt *} or {\tt ALL} can be
used in the second dimensions of the {\tt range-attr-stuff} for X.


                                                                \CODE
         REAL A(100, 100, 100)
!HPF$    DISTRIBUTE A(BLOCK, *, CYCLIC)

         CALL SUB( A(:,,:,1) )          ! Conforming
         CALL SUB( A(:,,1,:) )          ! Nonconforming
         CALL SUB( A(1,,:,:) )          ! Nonconforming
            ....

         SUBROUTINE SUB(X)
         REAL A(:, :)
!HPF$    INHERIT X
!HPF$    RANGE (BLOCK, *)
                                                                \EDOC

Given the range directive in the subroutine SUB, only the first call
to SUB is conforming. However, all three calls can be made conforming if
the range directive above is replaced by the following directive:

                                                                \CODE
!HPF$    RANGE (BLOCK, *), (BLOCK, CYCLIC), (*, CYCLIC)
                                                                \EDOC
         

\section{Shadow Width Declarations}

In compiling nearest-neighbor code, for example, in
discretizing partial differential equations or implementing
convolutions, a standard technique is to allocate storage on each
processor for the local array section that includes additional space
for the elements that have to be moved in from its neighboring
processors.  This additional storage is referred to as ``shadow
edges.''  There are conceptually two shadow edges for each array
dimension:  one at the low end of the local array section, and the
other at the high end.

In a single routine, the compiler can tell which arrays require shadow
edges, and allocate this additional space accordingly.  However, since
the width of the shadow area is dependent on the size of
the computational stencil being used, an array may require
different shadow widths in different routines. Thus, without
interprocedural analysis, an array argument may need to be 
copied into a space with the appropriate shadow width
on each procedure call. A similar data motion would be
required to copy the data back to its original location
on exit form the subroutine.
This unnecessary data motion can be avoided by allowing
the user to specify the required shadow width when the
array is declared.

Formally, the syntax for declaring shadow widths is as follows:

                                                                \BNF
extended-dist-format    \IS  BLOCK  [ ( int-expr [, shadow-spec-or-int-expr] ) ]
                        \OR  BLOCK  ( shadow-spec )
                        \OR  CYCLIC [ ( int-expr [, shadow-spec-or-int-expr] ) ]
                        \OR  CYCLIC  ( shadow-spec )
                        \OR GEN\_BLOCK (int-array [, shadow-spec-or-int-expr] )
                        \OR INDIRECT (int-array)
                        \OR  *

shadow-spec-or-int-expr \IS shadow-spec
                        \OR int-expr

shadow-spec             \IS SHADOW = int-expr
                        \OR LOW\_SHADOW = int-expr [, HIGH\_SHADOW = int-expr]
                        \OR HIGH\_SHADOW = int-expr [, LOW\_SHADOW = int-expr]
                                                                \FNB
\begin{constraints}
\item Any {\it int-expr} appearing in a {\it shadow-spec} or in a
{\it shadow-spec-or-int-expr} must be a constant {\it specification-expr} with
value greater than equal to {\it 0}.

\item
The absence of a {\it shadow-spec} or a
{\it shadow-spec-or-int-expr} is equivalent
to {\tt SHADOW = 0}.

\item The specification
{\tt SHADOW =  w} (where {\tt w} is an {\it int-expr}) is
equivalent to {\tt LOW\_SHADOW = w,  HIGH\_SHADOW = w}

\item
A {\it shadow-spec-or-int-expr} that is just an
{\it int-expr} (say {\tt w}) is
equivalent to {\tt SHADOW = w}.

\item
Specifying only {\tt LOW\_SHADOW} implies {\tt HIGH\_SHADOW = 0}.

\item
Specifying only {\tt HIGH\_SHADOW} implies {\tt LOW\_SHADOW = 0}.

\end{constraints}


Thus, the directive

                                                                \CODE
!HPF$    DISTRIBUTE(BLOCK(n, w))  ::  A 
                                                                \EDOC

\noindent
specifies that the array {\it A} is distributed by {\tt BLOCK(n)}
and is to have a
shadow width of {\it w} on both sides.
If {\it A} is a dummy argument, this gives the
compiler enough information to inhibit unnecessary data motion at
procedure calls.

The shadow width parameter can also be referenced by using the keyword
{\tt SHADOW}; this is really a preferred usage, and is necessary if the
distribution is {\tt BLOCK}, rather than {\tt BLOCK(n)}.  So for instance, the
following are equivalent:

                                                                \CODE
!HPF$    DISTRIBUTE(BLOCK(n, w))  ::  A 
!HPF$    DISTRIBUTE(BLOCK(n, SHADOW = w))  ::  A 
                                                                \EDOC

A {\tt BLOCK} distributed dimension with a shadow width would be
indicated simply as

                                                                \CODE
!HPF$    DISTRIBUTE(BLOCK(SHADOW = w))  ::  A 
                                                                \EDOC
In a similar fashion,
                                                                \CODE
!HPF$    DISTRIBUTE(CYCLIC(n, w))  ::  A 
!HPF$    DISTRIBUTE(CYCLIC(n, SHADOW = w))  ::  A 
                                                                \EDOC

\noindent
are both equivalent and refer to a {\tt CYCLIC(n)} distribution with a
shadow width of {\it w}.

Using the keywords 
{\tt LOW\_SHADOW} and {\tt HIGH\_SHADOW}, different
shadow widths can be specified for the low end and high end
of a dimension. For example:
                                                                \CODE
         REAL, DIMENSION (1000) :: A
!HPF$    DISTRIBUTE(BLOCK(LOW_SHADOW = 1, HIGH_SHADOW = 2))  ::  A 
        ....
        FORALL (i = 2, 998)
            A(i) = 0.25* (A(i) + A(i-1) + A(i+1) + A(i+2))
                                                                \EDOC
\noindent
specifies that only one non-local element is needed at the lower end
while two are needed at the high end.
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Date: Thu, 15 Aug 1996 11:32:34 -0700 (PDT)
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I will be attempting to assemble the latest draft of the HPF
document tomorrow.  I have much of it already - but am still
missing a few pieces.  If there is any way that even draft-stage
chapters can arrive in time, that would be helpful.  Please send
anything to me as well as Chuck.  Guy has offered to look at generating
syntax chapters for us - and I will be sending him the assembled draft.
    -mary-

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From owner-hpff-doc  Thu Aug 15 14:34:44 1996
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Date: Thu, 15 Aug 1996 14:34:44 -0500 (CDT)
Message-Id: <199608151934.OAA12306@cs.rice.edu>
From: offner@hpc.pko.dec.com (Carl Offner)
Subject: hpff-doc: mapping-subr.tex (again)
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% File: mapping-subr.tex

% Contents:
% Mapping constructs for dummy arguments for HPF 2.0 document,
% including
%       interface rules
%       INHERIT
%
% If you don't have LaTeX2e available, uncomment the next three lines:
%\def\emph#1{{\em #1}}
%\def\texttt#1{{\tt #1}}
%\def\textit#1{{\it #1}}

% Revision history:
% Aug-13-96     Edit by Carl Offner, Digital.  Some clarifications and
%               corrections of typos, based on suggestions from Rob
%               Schreiber.
%
% Aug-01-96     Edit by Carl Offner, Digital.  Based on 
%               decisions taken at the July HPFF meeting,
%               i)  DISTRIBUTE is no longer allowed on INHERITed
%                   arguments.
%               ii) The section describing when an explicit interface
%                   is not needed when arguments are explicitly mapped
%                   has been vastly tightened up.
%               In addition, descriptive syntax has been more clearly
%               identified as being left in purely for backward
%               compatibility; and the TERPSICHORE-FRUG example has
%               been reworked.
%
% Jun-03-96     Edit by Carl Offner, Digital.
%               Rearrangements, many edits, and two new sections (an
%               introduction and the section on when an explicit
%               interface is necessary).
%
% May-10-96     Created by Charles Koelbel, Rice University
%               (from HPF 1.2 document and HPF 2.0 proposals)

\chapter{Data Mapping in Subprogram Interfaces}
\label{ch-mapping-subr}

{\em
Comments on this chapter should be directed to 
Piyush Mehrotra ({\tt pm@icase.edu}), 
Carl Offner ({\tt offner@hpc.pko.dec.com}), 
Guy Steele ({\tt Guy.Steele@east.sun.com}),
and \\
{\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Mapping in Subprogram Calls}'' as the
{\tt Subject:} line.
\par
}


\bigskip  %% Take this out in the final document.

\emph{In this chapter, phrases such as ``it is the responsibility of
  the called subprogram to remap the argument'' are constraints on the
  implementation (i.e., on the generated code produced by the
  compiler), not on the source code produced by the programmer.}



\section{Introduction}
\label{mapsub:introduction}

\emph{This introduction gives an overview of the ways in which mapping
directives interact with argument passing to subprograms.  The
language used here, however, is not definitive; the subsequent
sections of this chapter contain the authoritative rules.}

In addition to the data mapping features described in
Chapter~\ref{ch-mapping-base}, HPF allows a number of options for
describing the mapping of dummy arguments to subprograms.

The mapping of each such dummy argument may be related to the mapping
of its associated actual argument in the calling main program or
procedure (the ``caller'') in several different ways.  To allow for
this, mapping directives applied to dummy arguments can have three
different syntactic forms: \emph{prescriptive}, \emph{descriptive},
and \emph{transcriptive}.

HPF provides these three forms to allow the programmer either to
specify that the data is to be left in place, or to specify that
during the execution of the call the data must be automatically
remapped into a new and presumably more efficient mapping for the
duration of the execution of the called subprogram.

The meaning of these forms is as follows:

\begin{description}
  
\item[prescriptive] The directive describes the mapping of the dummy.
  However, the actual as passed may not have this mapping.  \emph{If
  it does not}, it is the responsibility of the called subprogram to
  remap the argument as specified, and to restore the original mapping
  on exit.  (However, see the discussion on explicit interfaces and
  remapping below.)

  Prescriptive directives are syntactically identical to directives
  occurring elsewhere in the program.  For instance, if \texttt{A} is
  a dummy argument,

                                                                \CODE
!HPF$ DISTRIBUTE A (BLOCK, CYCLIC)
                                                                \EDOC
  is a prescriptive directive.
  
\item[descriptive] The directive describes the mapping of the dummy.
  It is the responsibility of the caller to insure that the actual as
  passed has this mapping.  (Similarly, remapping to restore the
  original mapping on exit is also done by the caller.)

  Descriptive directives look like prescriptive directives, except
  that an asterisk precedes the description.  For instance,
                                                                \CODE
!HPF$ DISTRIBUTE A *(BLOCK, CYCLIC)
                                                                \EDOC
  is a descriptive directive.
  
\item[transcriptive] The mapping is unspecified.  The called
  subprogram must accept the mapping of the argument as it is passed.
  (Of course this means that the caller must pass this mapping
  information at run-time.)
  
  Transcriptive directives are written with a single asterisk for 
  distributions and processor arrays; for instance
                                                                \CODE
!HPF$ DISTRIBUTE A *
                                                                \EDOC
  is a transcriptive directive.  The \texttt{INHERIT} directive
  (see Section~\ref{INHERIT-SECTION}) is used to specify a transcriptive
  alignment.

\end{description}

Both distribution formats and processor arrangements can be specified
prescriptively, descriptively, or transcriptively.  Alignment is more
complicated, because of the need to specify the template with which
the dummy is aligned.  This template may be unspecified (in this case
of course there is no \texttt{ALIGN} directive), in which case it is
the \emph{natural template} of the dummy.  (``Natural template'' is
defined in Section~\ref{mapsub:templates} below.)  Otherwise, one of
the following disjoint possibilities must be true:

\begin{itemize}

\item The template is explicitly specified by a prescriptive ALIGN directive.

\item The template is explicitly specified by a descriptive ALIGN directive.
  
\item The template is \emph{inherited}.  This is specified by giving
  the dummy the \texttt{INHERIT} attribute (described in
  Section~\ref{INHERIT-SECTION} below).  This implicitly specifies the
  template to be a copy of the template with which the corresponding
  actual argument is ultimately aligned; further, the alignment of the
  dummy with that template is the same as that of the corresponding
  actual.  This is in effect a transcriptive form of alignment.

\end{itemize}

This is restated more precisely in Section~\ref{mapsub:templates}
below.

If remapping is necessary at a subprogram interface, this fact must be
visible in the caller.  This is a consequence of the requirements for
explicit interfaces in Section~\ref{mapsub:ExplicitInterfaces}.

As a result of this, an implementation may choose to have all
necessary remapping done by the caller.  This in effect eliminates the
distinction between prescriptive and descriptive mappings, and
eliminates the need for the descriptive form of the directives.

While both prescriptive and descriptive syntactic forms remain in this
document, and while they are each treated in this chapter, it is fair
to say that the descriptive syntax is at this point maintained only
for backwards compatibility.

\begin{users}
  Although it is possible to write some combinations of mapping
  directives that are partially prescriptive and partially
  transcriptive, for instance, there is probably no virtue to so
  doing.  The point of these directives is to enable the compiler to
  handle any necessary remapping correctly and efficiently.  Now
  remapping can happen for one or more of the following reasons:

  \begin{itemize}
  \item  to make the alignment of the actual and the dummy agree;
  \item  to make the distribution of the actual and the dummy agree;
  \item  to make the processor array of the actual and the dummy agree.
  \end{itemize}

  For most machines, there is no real difference in the cost of
  remapping for any of these reasons.  It is therefore a better
  practice in general to make a mapping either purely transcriptive,
  purely prescriptive, or purely descriptive.

  While transcriptive mappings can be useful in writing libraries,
  they impose a run-time cost on the subprogram.  They should
  therefore be avoided in normal user code.
\end{users}

\section{What Remapping is Required, and Who Does It}

If there is an explicit interface for the called subprogram and that
interface contains prescriptive or descriptive mapping directives for
a dummy argument, and if a remapping of the corresponding actual
argument is necessary, the call should proceed as if the data was
copied to a temporary variable to match the mapping of the dummy
argument as expressed by the directives in the explicit interface.
The template of the dummy will then be as declared in the interface.

If in such a case the mapping directives are descriptive, then it is
the responsibility of the caller to perform the necessary remapping.
That is, the caller must provide an actual argument matching such
directives, so that the descriptive directives correctly describe the
dummy arguments to the subprogram.

\begin{implementors}
In fact, an implementation may choose to have \emph{all} necessary
remapping done by the caller.
\end{implementors}

If there is no explicit interface, then no remapping will be
necessary; this is a consequence of the requirements in
Section~\ref{mapsub:ExplicitInterfaces}.

An overriding principle is that \emph{any remapping of arguments is
not visible to the caller}.  That is, when the subprogram returns and
the caller resumes execution, all objects accessible to the caller
after the call are mapped exactly as they were before the call.  It is
not possible for a procedure to change the mapping of any object in a
manner visible to its caller.

\section{Distributions and Processor Arrangements}
\label{mapsub:DistProcArr}

In a \texttt{DISTRIBUTE} directive where every \textit{distributee} is
a dummy argument, either the \textit{dist-format-clause} or the
\textit{dist-target}, or both, may begin with, or consist of, an
asterisk.

\begin{itemize}
  
\item Without an asterisk, a \textit{dist-format-clause} or
  \textit{dist-target} is prescriptive; the clause describes a
  distribution and constitutes a request of the language processor to
  make it so.  This might entail the subprogram remapping or copying
  the actual argument on entry at run time in order to satisfy the
  requested distribution for the dummy.
  
\item Starting with an asterisk, a \textit{dist-format-clause} or
  \textit{dist-target} is descriptive; the clause describes a
  distribution and constitutes an assertion to the language processor
  that on entry to the subprogram it will already be so.  The
  programmer claims that, for every call to the subprogram, the actual
  argument will be such that the stated distribution already describes
  the mapping of that data.  (The intent is that if the argument is
  passed by reference, no movement of the data \emph{by the
  subprogram} will be necessary at run time.  All this is under the
  assumption that the language processor has observed all other
  directives.  While a conforming HPF language processor is not
  required to obey mapping directives, it should handle descriptive
  directives with the understanding that their implied assertions are
  relative to this assumption.)

\item Consisting of only an asterisk, a \textit{dist-format-clause} or
  \textit{dist-target} is transcriptive; the clause says nothing about
  the distribution but constitutes a request of the language processor
  to copy that aspect of the distribution from that of the actual
  argument.  (The intent is that if the argument is passed by
  reference, no movement of the data will be necessary at run time.)
\end{itemize}

It is possible that, in a single \texttt{DISTRIBUTE} directive, the
\textit{dist-format-clause} might have an asterisk but not the
\textit{dist-target}, or vice versa.

\subsection{Examples}

These examples of \texttt{DISTRIBUTE} directives for dummy arguments
illustrate the various combinations:

                                                                        \CODE
!HPF$ DISTRIBUTE URANIA (CYCLIC) ONTO GALILEO
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{URANIA} to have a \texttt{CYCLIC} distribution on the
processor arrangement \texttt{GALILEO}.
                                                                        \CODE
!HPF$ DISTRIBUTE POLYHYMNIA * ONTO ELVIS
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{POLYHYMNIA} to be distributed onto the processor arrangement
\texttt{ELVIS}, using whatever distribution format it currently has
(which might be on some other processor arrangement).
                                                                        \CODE
!HPF$ DISTRIBUTE THALIA *(CYCLIC) ONTO FLIP
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{THALIA} to have a \texttt{CYCLIC} distribution on the
processor arrangement \texttt{FLIP}; \texttt{THALIA} already has a
cyclic distribution, though it might be on some other processor
arrangement.
                                                                        \CODE
!HPF$ DISTRIBUTE CALLIOPE (CYCLIC) ONTO *HOMER
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{CALLIOPE} to have a \texttt{CYCLIC} distribution on the
processor arrangement \texttt{HOMER}; \texttt{CALLIOPE} is already
distributed onto \texttt{HOMER}, though it might be with some other
distribution format.
                                                                        \CODE
!HPF$ DISTRIBUTE MELPOMENE * ONTO *EURIPIDES
                                                                        \EDOC
\texttt{MELPOMENE} is asserted to already be distributed onto
\texttt{EURIPIDES}; use whatever distribution format the actual
argument had so, if possible, no data movement should occur.
                                                                        \CODE
!HPF$ DISTRIBUTE CLIO *(CYCLIC) ONTO *HERODOTUS
                                                                        \EDOC
\texttt{CLIO} is asserted to already be distributed \texttt{CYCLIC}
onto \texttt{HERODOTUS} so, if possible, no data movement should
occur.
                                                                        \CODE
!HPF$ DISTRIBUTE EUTERPE (CYCLIC) ONTO *
                                                                        \EDOC
The language processor should do whatever it takes to cause
\texttt{EUTERPE} to have a \texttt{CYCLIC} distribution onto whatever
processor arrangement the actual was distributed onto.
                                                                        \CODE
!HPF$ DISTRIBUTE ERATO * ONTO *
                                                                        \EDOC
The mapping of \texttt{ERATO} should not be changed from that of the
actual argument.
                                                                        \CODE
!HPF$ DISTRIBUTE ARTHUR_MURRAY *(CYCLIC) ONTO *
                                                                        \EDOC
\texttt{ARTHUR_MURRAY} is asserted to already be distributed
\texttt{CYCLIC} onto whatever processor arrangement the actual
argument was distributed onto, and no data movement should occur.

Also note that \texttt{DISTRIBUTE ERATO * ONTO *} does not mean the
same thing as
                                                                        \CODE
!HPF$ DISTRIBUTE ERATO *(*) ONTO *
                                                                        \EDOC
This latter means:  \texttt{ERATO} is asserted to already be distributed
\texttt{*} (that is, on-processor) onto whatever processor arrangement the
actual was distributed onto.  The processor arrangement is necessarily
scalar in this case.

\subsection{What Happens When a Clause is Omitted}

One may omit either the \textit{dist-format-clause} or the
\textit{dist-onto-clause} for a dummy argument.  This is understood as
follows:

If the dummy argument has the \texttt{INHERIT} attribute (see
Section~\ref{INHERIT-SECTION}), then no distribution directive is
allowed in any case:  the distribution as well as the alignment is
inherited from the actual argument.

In any other case in which distribution information is omitted, the
compiler may choose the distribution format or a target processor
arrangement arbitrarily.

Here are two examples:
                                                                         \CODE
!HPF$ DISTRIBUTE WHEEL_OF_FORTUNE *(CYCLIC)
                                                                         \EDOC
\texttt{WHEEL_OF_FORTUNE} is asserted to already be \texttt{CYCLIC}.
As long as it is kept \texttt{CYCLIC}, it may be remapped onto some
other processor arrangement, but there is no reason to.
                                                                          \CODE
!HPF$ DISTRIBUTE ONTO *TV :: DAVID_LETTERMAN
                                                                          \EDOC
\texttt{DAVID_LETTERMAN} is asserted to already be distributed
on \texttt{TV} in some fashion.  The distribution format may be
changed as long as \texttt{DAVID_LETTERMAN} is kept on \texttt{TV}.
(Note that this declaration must be made in attributed form; the
statement form

                                                                        \CODE
!HPF$ DISTRIBUTE DAVID_LETTERMAN ONTO *TV         !Nonconforming
                                                                        \EDOC
does not conform to the syntax for a \texttt{DISTRIBUTE} directive.)




\section{Alignment}

\subsection{The Template of the Dummy Argument}
\label{mapsub:templates}

Here we describe precisely how the template with which the dummy
argument is ultimately aligned is arrived at.

First, templates are not passed through the subprogram argument
interface.  A dummy argument and its corresponding actual argument may
be aligned to the same template only if that template is accessible in
both the caller and the called subprogram either through host
association or use association.

In any other case, the template with which a dummy argument is aligned is
always distinct from the template with which the actual argument is
aligned, though it may be a copy (see Section \ref{INHERIT-SECTION}).
On exit from a procedure, an HPF implementation arranges that the
actual argument is aligned with the same template with which it was
aligned before the call.

The template of the dummy argument is arrived at in one of three ways:

\begin{itemize}
\item If the dummy argument appears explicitly as an \textit{alignee}
  in an \texttt{ALIGN} directive, its template is the
  \textit{align-target} if the \textit{align-target} is a template;
  otherwise its template is the template with which the
  \textit{align-target} is ultimately aligned.
  
\item If the dummy argument is not explicitly aligned and does not
  have the \texttt{INHERIT} attribute (described in
  Section~\ref{INHERIT-SECTION} below), then the template has the same
  shape and bounds as the dummy argument; this is called the
  \textit{natural template} for the dummy.

  (Thus, all the examples in Section~\ref{mapsub:DistProcArr} use
  the natural template.)

\item If the dummy argument is not explicitly aligned and does have
  the \texttt{INHERIT} attribute, then the template is ``inherited'' from
  the actual argument according to the following rules:

  \begin{itemize}
    
  \item If the actual argument is a whole array, the template of the
    dummy is a copy of the template with which the actual argument is
    ultimately aligned.
    
  \item If the actual argument is an array section of array \(A\)
    where no subscript is a vector subscript, then the template of the
    dummy is a copy of the template with which \(A\) is ultimately
    aligned.

  \item If the actual argument is any other expression, the shape
    and distribution of the template may be chosen arbitrarily by
    the language processor (and therefore the programmer cannot know
    anything \textit{a priori} about its distribution).

  \end{itemize}
  
  In all of these cases, we say that the dummy has an \textit{inherited
  template}.

\end{itemize}


\subsection{The INHERIT Directive}
\label{INHERIT-SECTION}

The \texttt{INHERIT} directive specifies that a dummy argument should be
aligned to a copy of the template of the corresponding actual argument
in the same way that the actual argument is aligned.

                                                                        \BNF
inherit-directive      \IS  INHERIT dummy-argument-name-list
                                                                        \FNB

The \texttt{INHERIT} directive causes the named subprogram dummy
arguments to have the \texttt{INHERIT} attribute.  Only dummy
arguments may have the \texttt{INHERIT} attribute.  An object must not
have both the \texttt{INHERIT} attribute and the \texttt{ALIGN}
attribute.  The \texttt{INHERIT} directive may appear only in a
\textit{specification-part} of a scoping unit.

If a dummy argument has the \texttt{TARGET} attribute and no explicit
mapping attributes, then the \texttt{INHERIT} attribute is implicitly
assumed.  (See section~\ref{mapsub:pointers}.)

The \texttt{INHERIT} attribute specifies that the template for a dummy
argument should be inherited, by making a copy of the template of the
actual argument.  Moreover, no other explicit mapping directive may
appear for an argument with the \texttt{INHERIT} attribute: the
\texttt{INHERIT} attribute implies a distribution of
\texttt{DISTRIBUTE~*~ONTO~*} for the inherited template.  Thus, the
net effect is to tell the compiler to leave the data exactly where it
is, and not attempt to remap the actual argument.  The dummy argument
will be mapped in exactly the same manner as the actual argument; the
subprogram must be compiled in such a way as to work correctly no
matter how the actual argument may be mapped onto abstract processors.

\subsubsection{Examples}

Here is a straightforward example of the use of \texttt{INHERIT}:

                                            \CODE

      REAL DOUGH(100)
!HPF$ DISTRIBUTE DOUGH(BLOCK(10))
      CALL PROBATE( DOUGH(7:23:2) )
      ...
      SUBROUTINE PROBATE(BREAD)
      REAL BREAD(9)
!HPF$ INHERIT BREAD
                                             \EDOC

The inherited template of \texttt{BREAD} has shape [100]; element 
\texttt{BREAD(I)} is aligned with element 5 + 2*I of the inherited
template, and that template has a \texttt{BLOCK(10)} distribution.


More complicated examples can easily be constructed.  It is important
to bear in mind that the inherited template may have a different rank
than the rank of the dummy, and it may even have a different rank than
the rank of the actual.  For instance, one might have a program
containing the following:

                                                \CODE
      REAL A(100,100)
!HPF$ TEMPLATE T(100,100,100)
!HPF$ DISTRIBUTE T(BLOCK,CYCLIC,*)
!HPF$ ALIGN A(I,J) with T(J,3,I)
      CALL SUBR(A(:,7))
      ...
      SUBROUTINE SUBR(D)
      REAL D(100)
!HPF$ INHERIT D
                                                 \EDOC

In this case, the dummy \texttt{D} has rank 1.  It corresponds to a
1-dimensional section of a 2-dimensional actual \texttt{A} which in
turn is aligned with a 2-dimensional section of a 3-dimensional
template \texttt{T}.  The template of \texttt{D} is a copy of this
three-dimensional template.  \texttt{D} is aligned with the section
\texttt{(7, 3, :)} of this inherited template.  Thus, the ``visible''
dimension of the dummy \texttt{D} is distributed \texttt{*}, although
if the call statement had been

                                                \CODE
      CALL SUBR(A(7,:))
                                                 \EDOC

\noindent
for instance, the ``visible'' dimension of the dummy would be
distributed \texttt{BLOCK}.


\subsection{ALIGN Directives}

The presence or absence of an asterisk at the start of an
\textit{align-spec} has the same meaning as in a
\textit{dist-format-clause}: it specifies whether the \texttt{ALIGN}
directive is descriptive or prescriptive, respectively.

If an \textit{align-spec} that does not begin with \texttt{*} is
applied to a dummy argument, the meaning is that the dummy argument
will be forced to have the specified alignment on entry to the
subprogram.  This may require either the caller or the subprogram to
temporarily remap the data of the actual argument or a copy thereof.

Note that a dummy argument may also be used as an \textit{align-target}.
                                                                        \CODE
      SUBROUTINE NICHOLAS(TSAR,CZAR)
      REAL, DIMENSION(1918) :: TSAR,CZAR
!HPF$ INHERIT :: TSAR
!HPF$ ALIGN WITH TSAR :: CZAR
                                                                        \EDOC

In this example the first dummy argument, \texttt{TSAR}, remains
aligned with the corresponding actual argument, while the second dummy
argument, \texttt{CZAR}, is forced to be aligned with the first dummy
argument.  If the two actual arguments are already aligned, no
remapping of the data will be required at run time.  If they are not,
some remapping will take place.

If the \textit{align-spec} begins with ``\texttt{*}'', then the
\textit{alignee} must be a dummy argument.  The ``\texttt{*}''
indicates that the \texttt{ALIGN} directive constitutes a guarantee on
the part of the programmer that, on entry to the subprogram, the
indicated alignment will already be satisfied by the dummy argument,
without any action to remap it required (on the part of the
subprogram) at run time.  For example:

                                                                        \CODE
      SUBROUTINE GRUNGE(PLUNGE,SPONGE)
      REAL PLUNGE(1000),SPONGE(1000)
!HPF$ INHERIT SPONGE
!HPF$ ALIGN PLUNGE WITH *SPONGE
                                                                        \EDOC

This asserts that, for every \texttt{J} in the range \texttt{1:1000},
on entry to subroutine \texttt{GRUNGE}, the directives in the program
have specified that \texttt{PLUNGE(J)} is currently mapped to the same
abstract processor as \texttt{SPONGE(J)}.

The intent is that if the language processor has in fact honored the
directives, then no interprocessor communication on the part of the
subprogram will be required to achieve the specified alignment.  As
usual, if an implementation performs all remapping in the caller, a
prescriptive form of the \texttt{ALIGN} directive would mean exactly
the same thing.

It is not permitted to say simply ``\texttt{ALIGN WITH *}''; an
\textit{align-target} must follow the asterisk.  (The proper way to
say ``accept any alignment'' is \texttt{INHERIT}.)

If a dummy argument has no explicit \texttt{ALIGN} or
\texttt{DISTRIBUTE} attribute, then the compiler provides an implicit
alignment and distribution specification, one that could have been
described explicitly without any ``assertion asterisks''.

\subsubsection{Example}

Without using \texttt{INHERIT}, explicit alignment of a dummy argument
may be necessary to insure that no remapping takes place at the
subprogram boundary.  Here is an example:

                                                                       \CODE
      LOGICAL FRUG(128)
!HPF$ PROCESSORS DANCE_FLOOR(16)
!HPF$ DISTRIBUTE (BLOCK) ONTO DANCE_FLOOR::FRUG
      CALL TERPSICHORE(FRUG(1:40:3))
                                                                        \EDOC

The array section \texttt{FRUG(1:40:3)} is mapped onto abstract
processors in the following manner:
\begin{center}
\setlength{\unitlength}{0.01in}
\begin{picture}(560,225)(0,0)
\put(0,200){\makebox(35,25){\small\rm 1}}
\put(35,200){\makebox(35,25){\small\rm 2}}
\put(70,200){\makebox(35,25){\small\rm 3}}
\put(105,200){\makebox(35,25){\small\rm 4}}
\put(140,200){\makebox(35,25){\small\rm 5}}
\put(175,200){\makebox(35,25){\small\rm 6}}
\put(210,200){\makebox(35,25){\small\rm 7}}
\put(245,200){\makebox(35,25){\small\rm 8}}
\put(280,200){\makebox(35,25){\small\rm 9}}
\put(315,200){\makebox(35,25){\small\rm 10}}
\put(350,200){\makebox(35,25){\small\rm 11}}
\put(385,200){\makebox(35,25){\small\rm 12}}
\put(420,200){\makebox(35,25){\small\rm 13}}
\put(455,200){\makebox(35,25){\small\rm 14}}
\put(490,200){\makebox(35,25){\small\rm 15}}
\put(525,200){\makebox(35,25){\small\rm 16}}
\thinlines
\multiput(0,25)(0,25){7}{\line(1,0){560}}
\thicklines
\multiput(0,0)(0,200){2}{\line(1,0){560}}
\multiput(0,0)(35,0){17}{\line(0,1){200}}
\put(0,175){\makebox(35,25){\tt 1}}
\put(0,100){\makebox(35,25){\tt 4}}
\put(0,25){\makebox(35,25){\tt 7}}
\put(35,150){\makebox(35,25){\tt 10}}
\put(35,75){\makebox(35,25){\tt 13}}
\put(35,0){\makebox(35,25){\tt 16}}
\put(70,125){\makebox(35,25){\tt 19}}
\put(70,50){\makebox(35,25){\tt 22}}
\put(105,175){\makebox(35,25){\tt 25}}
\put(105,100){\makebox(35,25){\tt 28}}
\put(105,25){\makebox(35,25){\tt 31}}
\put(140,150){\makebox(35,25){\tt 34}}
\put(140,75){\makebox(35,25){\tt 37}}
\put(140,0){\makebox(35,25){\tt 40}}
\end{picture}
\end{center}

Suppose first that the interface to the subroutine
\texttt{TERPSICHORE} looks like this:

                                                                        \CODE
      SUBROUTINE TERPSICHORE(FOXTROT)
      LOGICAL FOXTROT(:)
!HPF$ INHERIT FOXTROT
                                                                        \EDOC
The template of \texttt{FOXTROT} is a copy of the 128 element
template of the whole array \texttt{FRUG}.  The template is mapped like this:

\begin{center}
\setlength{\unitlength}{0.01in}
\begin{picture}(560,225)(0,0)
\put(0,200){\makebox(35,25){\small\rm 1}}
\put(35,200){\makebox(35,25){\small\rm 2}}
\put(70,200){\makebox(35,25){\small\rm 3}}
\put(105,200){\makebox(35,25){\small\rm 4}}
\put(140,200){\makebox(35,25){\small\rm 5}}
\put(175,200){\makebox(35,25){\small\rm 6}}
\put(210,200){\makebox(35,25){\small\rm 7}}
\put(245,200){\makebox(35,25){\small\rm 8}}
\put(280,200){\makebox(35,25){\small\rm 9}}
\put(315,200){\makebox(35,25){\small\rm 10}}
\put(350,200){\makebox(35,25){\small\rm 11}}
\put(385,200){\makebox(35,25){\small\rm 12}}
\put(420,200){\makebox(35,25){\small\rm 13}}
\put(455,200){\makebox(35,25){\small\rm 14}}
\put(490,200){\makebox(35,25){\small\rm 15}}
\put(525,200){\makebox(35,25){\small\rm 16}}
\thinlines
\multiput(0,25)(0,25){7}{\line(1,0){560}}
\thicklines
\multiput(0,0)(0,200){2}{\line(1,0){560}}
\multiput(0,0)(35,0){17}{\line(0,1){200}}
\put(0,175){\makebox(35,25){\tt 1}}
\put(0,150){\makebox(35,25){\tt 2}}
\put(0,125){\makebox(35,25){\tt 3}}
\put(0,100){\makebox(35,25){\tt 4}}
\put(0,75){\makebox(35,25){\tt 5}}
\put(0,50){\makebox(35,25){\tt 6}}
\put(0,25){\makebox(35,25){\tt 7}}
\put(0,0){\makebox(35,25){\tt 8}}
\put(35,175){\makebox(35,25){\tt 9}}
\put(35,150){\makebox(35,25){\tt 10}}
\put(35,125){\makebox(35,25){\tt 11}}
\put(35,100){\makebox(35,25){\tt 12}}
\put(35,75){\makebox(35,25){\tt 13}}
\put(35,50){\makebox(35,25){\tt 14}}
\put(35,25){\makebox(35,25){\tt 15}}
\put(35,0){\makebox(35,25){\tt 16}}
\put(70,175){\makebox(35,25){\tt 17}}
\put(70,150){\makebox(35,25){\tt 18}}
\put(70,125){\makebox(35,25){\tt 19}}
\put(70,100){\makebox(35,25){\tt 20}}
\put(70,75){\makebox(35,25){\tt 21}}
\put(70,50){\makebox(35,25){\tt 22}}
\put(70,25){\makebox(35,25){\tt 23}}
\put(70,0){\makebox(35,25){\tt 24}}
\put(105,175){\makebox(35,25){\tt 25}}
\put(105,150){\makebox(35,25){\tt 26}}
\put(105,125){\makebox(35,25){\tt 27}}
\put(105,100){\makebox(35,25){\tt 28}}
\put(105,75){\makebox(35,25){\tt 29}}
\put(105,50){\makebox(35,25){\tt 30}}
\put(105,25){\makebox(35,25){\tt 31}}
\put(105,0){\makebox(35,25){\tt 32}}
\put(140,175){\makebox(35,25){\tt 33}}
\put(140,150){\makebox(35,25){\tt 34}}
\put(140,125){\makebox(35,25){\tt 35}}
\put(140,100){\makebox(35,25){\tt 36}}
\put(140,75){\makebox(35,25){\tt 37}}
\put(140,50){\makebox(35,25){\tt 38}}
\put(140,25){\makebox(35,25){\tt 39}}
\put(140,0){\makebox(35,25){\tt 40}}
\put(175,175){\makebox(35,25){\tt 41}}
\put(175,150){\makebox(35,25){\tt 42}}
\put(175,125){\makebox(35,25){\tt 43}}
\put(175,100){\makebox(35,25){\tt 44}}
\put(175,75){\makebox(35,25){\tt 45}}
\put(175,50){\makebox(35,25){\tt 46}}
\put(175,25){\makebox(35,25){\tt 47}}
\put(175,0){\makebox(35,25){\tt 48}}
\put(210,175){\makebox(35,25){\tt 49}}
\put(210,150){\makebox(35,25){\tt 50}}
\put(210,125){\makebox(35,25){\tt 51}}
\put(210,100){\makebox(35,25){\tt 52}}
\put(210,75){\makebox(35,25){\tt 53}}
\put(210,50){\makebox(35,25){\tt 54}}
\put(210,25){\makebox(35,25){\tt 55}}
\put(210,0){\makebox(35,25){\tt 56}}
\put(245,175){\makebox(35,25){\tt 57}}
\put(245,150){\makebox(35,25){\tt 58}}
\put(245,125){\makebox(35,25){\tt 59}}
\put(245,100){\makebox(35,25){\tt 60}}
\put(245,75){\makebox(35,25){\tt 61}}
\put(245,50){\makebox(35,25){\tt 62}}
\put(245,25){\makebox(35,25){\tt 63}}
\put(245,0){\makebox(35,25){\tt 64}}
\put(280,175){\makebox(35,25){\tt 65}}
\put(280,150){\makebox(35,25){\tt 66}}
\put(280,125){\makebox(35,25){\tt 67}}
\put(280,100){\makebox(35,25){\tt 68}}
\put(280,75){\makebox(35,25){\tt 69}}
\put(280,50){\makebox(35,25){\tt 70}}
\put(280,25){\makebox(35,25){\tt 71}}
\put(280,0){\makebox(35,25){\tt 72}}
\put(315,175){\makebox(35,25){\tt 73}}
\put(315,150){\makebox(35,25){\tt 74}}
\put(315,125){\makebox(35,25){\tt 75}}
\put(315,100){\makebox(35,25){\tt 76}}
\put(315,75){\makebox(35,25){\tt 77}}
\put(315,50){\makebox(35,25){\tt 78}}
\put(315,25){\makebox(35,25){\tt 79}}
\put(315,0){\makebox(35,25){\tt 80}}
\put(350,175){\makebox(35,25){\tt 81}}
\put(350,150){\makebox(35,25){\tt 82}}
\put(350,125){\makebox(35,25){\tt 83}}
\put(350,100){\makebox(35,25){\tt 84}}
\put(350,75){\makebox(35,25){\tt 85}}
\put(350,50){\makebox(35,25){\tt 86}}
\put(350,25){\makebox(35,25){\tt 87}}
\put(350,0){\makebox(35,25){\tt 88}}
\put(385,175){\makebox(35,25){\tt 89}}
\put(385,150){\makebox(35,25){\tt 90}}
\put(385,125){\makebox(35,25){\tt 91}}
\put(385,100){\makebox(35,25){\tt 92}}
\put(385,75){\makebox(35,25){\tt 93}}
\put(385,50){\makebox(35,25){\tt 94}}
\put(385,25){\makebox(35,25){\tt 95}}
\put(385,0){\makebox(35,25){\tt 96}}
\put(420,175){\makebox(35,25){\tt 97}}
\put(420,150){\makebox(35,25){\tt 98}}
\put(420,125){\makebox(35,25){\tt 99}}
\put(420,100){\makebox(35,25){\tt 100}}
\put(420,75){\makebox(35,25){\tt 101}}
\put(420,50){\makebox(35,25){\tt 102}}
\put(420,25){\makebox(35,25){\tt 103}}
\put(420,0){\makebox(35,25){\tt 104}}
\put(455,175){\makebox(35,25){\tt 105}}
\put(455,150){\makebox(35,25){\tt 106}}
\put(455,125){\makebox(35,25){\tt 107}}
\put(455,100){\makebox(35,25){\tt 108}}
\put(455,75){\makebox(35,25){\tt 109}}
\put(455,50){\makebox(35,25){\tt 110}}
\put(455,25){\makebox(35,25){\tt 111}}
\put(455,0){\makebox(35,25){\tt 112}}
\put(490,175){\makebox(35,25){\tt 113}}
\put(490,150){\makebox(35,25){\tt 114}}
\put(490,125){\makebox(35,25){\tt 115}}
\put(490,100){\makebox(35,25){\tt 116}}
\put(490,75){\makebox(35,25){\tt 117}}
\put(490,50){\makebox(35,25){\tt 118}}
\put(490,25){\makebox(35,25){\tt 119}}
\put(490,0){\makebox(35,25){\tt 120}}
\put(525,175){\makebox(35,25){\tt 121}}
\put(525,150){\makebox(35,25){\tt 122}}
\put(525,125){\makebox(35,25){\tt 123}}
\put(525,100){\makebox(35,25){\tt 124}}
\put(525,75){\makebox(35,25){\tt 125}}
\put(525,50){\makebox(35,25){\tt 126}}
\put(525,25){\makebox(35,25){\tt 127}}
\put(525,0){\makebox(35,25){\tt 128}}
\end{picture}
\end{center}

\noindent
\texttt{FOXTROT(I)} is aligned with element 3*I-2 of the template.

Suppose on the other hand that the interface to \texttt{TERPSICHORE} looks
like this:

                                                                        \CODE
      SUBROUTINE TERPSICHORE(FOXTROT)
      LOGICAL FOXTROT(:)
!HPF$ DISTRIBUTE FOXTROT(BLOCK)
                                                                        \EDOC


In this case, the template of \texttt{FOXTROT} is its natural
template; it has the same size 14 as \texttt{FOXTROT} itself.  The
actual argument, \texttt{FRUG(1:40:3)} is mapped to the 16 processors
in this manner:

\begin{center}
\begin{tabular}{cc}
Abstract  &  Elements \\
processor & of FRUG \\
1 & 1, 2, 3 \\
2 & 4, 5, 6 \\
3 & 7, 8 \\
4 & 9, 10, 11 \\
5 & 12, 13, 14 \\
6--16   &  none
\end{tabular}
\end{center}

That is, the original positions (in the template of the actual
argument) of the elements of the dummy are as follows:

\begin{center}
\setlength{\unitlength}{0.01in}
\begin{picture}(560,225)(0,0)
\put(0,200){\makebox(35,25){\small\rm 1}}
\put(35,200){\makebox(35,25){\small\rm 2}}
\put(70,200){\makebox(35,25){\small\rm 3}}
\put(105,200){\makebox(35,25){\small\rm 4}}
\put(140,200){\makebox(35,25){\small\rm 5}}
\put(175,200){\makebox(35,25){\small\rm 6}}
\put(210,200){\makebox(35,25){\small\rm 7}}
\put(245,200){\makebox(35,25){\small\rm 8}}
\put(280,200){\makebox(35,25){\small\rm 9}}
\put(315,200){\makebox(35,25){\small\rm 10}}
\put(350,200){\makebox(35,25){\small\rm 11}}
\put(385,200){\makebox(35,25){\small\rm 12}}
\put(420,200){\makebox(35,25){\small\rm 13}}
\put(455,200){\makebox(35,25){\small\rm 14}}
\put(490,200){\makebox(35,25){\small\rm 15}}
\put(525,200){\makebox(35,25){\small\rm 16}}
\thinlines
\multiput(0,25)(0,25){7}{\line(1,0){560}}
\thicklines
\multiput(0,0)(0,200){2}{\line(1,0){560}}
\multiput(0,0)(35,0){17}{\line(0,1){200}}
\put(0,175){\makebox(35,25){\tt 1}}
\put(0,100){\makebox(35,25){\tt 2}}
\put(0,25){\makebox(35,25){\tt 3}}
\put(35,150){\makebox(35,25){\tt 4}}
\put(35,75){\makebox(35,25){\tt 5}}
\put(35,0){\makebox(35,25){\tt 6}}
\put(70,125){\makebox(35,25){\tt 7}}
\put(70,50){\makebox(35,25){\tt 8}}
\put(105,175){\makebox(35,25){\tt 9}}
\put(105,100){\makebox(35,25){\tt 10}}
\put(105,25){\makebox(35,25){\tt 11}}
\put(140,150){\makebox(35,25){\tt 12}}
\put(140,75){\makebox(35,25){\tt 13}}
\put(140,0){\makebox(35,25){\tt 14}}
\end{picture}
\end{center}

This layout (3 elements on the first processor, 3 on the second, 2 on
the third, 3 on the fourth, \dots) cannot properly be described as a
\texttt{BLOCK} distribution.  Therefore, remapping will take place at
the call.

Remapping can be avoided without using \texttt{INHERIT} by explicitly
aligning the dummy to a declared template of size 128 distributed
\texttt{BLOCK}:

                                                                        \CODE
      SUBROUTINE TERPSICHORE(FOXTROT)
      LOGICAL FOXTROT(:)
!HPF$ PROCESSORS DANCE_FLOOR(16)
!HPF$ TEMPLATE, DISTRIBUTE(BLOCK) ONTO DANCE_FLOOR::GURF(128)
!HPF$ ALIGN FOXTROT(J) WITH GURF(3*J-2)
                                                                        \EDOC

\begin{users}
  The advantage of this technique is that, where it can be used, it
  gives the compiler more information; this information can often be
  used to generate more efficient code.
\end{users}

\section{Explicit Interfaces}
\label{mapsub:ExplicitInterfaces}

An explicit interface is required \emph{except} when all four of the
following conditions hold:

\begin{enumerate}

\item  Fortran does not require one, \emph{and}
  
\item No dummy argument is passed transcriptively or with the
  \texttt{INHERIT} attribute, \emph{and}

\item For each pair of corresponding actual and dummy arguments, either:

  \begin{enumerate}

  \item They are both implicitly mapped, or

  \item They are both explicitly mapped and the conditions in
    Section~\ref{mapsub:NoExplicitInterface} are satisfied.

  \end{enumerate}

  \emph{and}

\item For each pair of corresponding actual and dummy arguments, either:

  \begin{enumerate}

  \item Both are sequential, or

  \item Both are nonsequential.

  \end{enumerate}

\end{enumerate}

\begin{rationale}
  This has the following consequences:

  \begin{itemize}

  \item A plain Fortran program (i.e., with no HPF directives) will
    continue to be legal without the need to add additional interfaces.
    This is insured by items 1, 2, 3a, and 4a.
  
  \item If remapping is necessary, this fact will be visible to the
    caller.  Thus the implementation may choose to have all remapping
    performed by the caller.

  \end{itemize}
\end{rationale}

\begin{users}
  This requirement pushes the user strongly in the direction of always
  providing explicit interfaces.  This is a good thing---explicit
  interfaces allow many errors to be caught at compile-time and greatly
  speed up the process of robust software development.

  Note, that an explicit interface can be provided in three ways:

  \begin{enumerate}

  \item Module subprograms have an explicit interface.

  \item Contained subprograms have an explicit interface.

  \item An explicit interface may be provided by an interface block.

  \end{enumerate}

  In addition, an intrinsic procedure always has an explicit interface
  by definition.

  The idiomatic Fortran way of programming makes extensive use of
  modules; every subprogram, for instance, can be in a module.  This
  provides explicit interfaces automatically, with no extra effort on
  the part of the programmer.  It should very seldom be necessary to
  write an interface block.
\end{users}


\subsection{Explicit Mappings Without an Explicit Interface}
\label{mapsub:NoExplicitInterface}

When there is no explicit interface, the actual and dummy arguments
may still be explicitly mapped (but not transcriptively or with the
\texttt{INHERIT} attribute), as long as the conditions in this section
are satisfied.

\begin{users}
  These conditions are complex.  The important thing to realize is
  that you don't have to read any of this if you have an explicit
  interface.  So if there is any doubt in your mind, just make sure
  you have an explicit interface.
\end{users}

\begin{enumerate}
  
\item The actual argument must be a named object.  (So for instance,
  the actual argument cannot be an array section.)
  
\item The shapes of the ultimate align targets of the dummy and the
  actual must be the same.

\item Either

  \begin{enumerate}
  \item the ultimate align targets of the dummy and actual must not
    have been explicitly distributed, or
    
  \item the \texttt{DISTRIBUTE} directives specified for both ultimate
    align targets must

    \begin{enumerate}
    \item have a \textit{dist-onto-clause} specifying processor
      arrangements with the same shape; and
      
    \item specify a \textit{dist-format-clause} with the same
      \textit{dist-format}s in corresponding positions, except that a
      \textit{dist-format} of \texttt{BLOCK} is regarded as the same
      as a \textit{dist-format} of \texttt{BLOCK(\(n\))} if the the
      actual blocking size of the \texttt{BLOCK} distribution has the
      same value as \(n\); and the same for \texttt{CYCLIC} and
      \texttt{CYCLIC(\(n\))}.
    \end{enumerate}
  \end{enumerate}

\item Each dimension of the actual and dummy must correspond to the same
  dimension of their respective ultimate align targets, and
  corresponding elements of the actual and dummy must be aligned with
  the same corresponding elements of their respective ultimate align
  targets.
\end{enumerate}


\section{Restrictions on Pointers and Targets}
\label{mapsub:pointers}

If, on invocation of a procedure P: (a)~a dummy argument has the
\texttt{TARGET} attribute, and (b)~the corresponding actual argument
has the \texttt{TARGET} attribute and is not an array section with a
vector subscript (and therefore is an object A or a section of an
array A), then the program is not HPF-conforming unless:
\begin{enumerate}
\item No remapping of the actual argument occurs during the call; or
\item the remainder of program execution would be unaffected if
  \begin{enumerate}
  \item\label{first-item} each pointer associated with any portion of
    the dummy argument or with any portion of A during execution of P
    were to acquire undefined pointer association status on exit from
    P; and
  \item\label{second-item} each pointer associated with any portion of
    A before the call were to acquire undefined pointer association
    status on entry to P and, if not reassigned during execution of P,
    were to be restored on exit to the pointer association status it
    had before entry.
  \end{enumerate}
\end{enumerate}

Note that if a dummy argument has the \texttt{TARGET} attribute and no
explicit mapping attributes, then the \texttt{INHERIT} attribute is
implicitly assumed (see section~\ref{INHERIT-SECTION}); therefore no
remapping occurs for such a dummy argument and there is no problem.

\begin{rationale}
  These restrictions are made in order to support the following part
  of the Fortran standard (in Section 12.4.1.1 of that document) in
  the face of implicit remapping across the subprogram interface:
  \begin{quote}
    If the dummy argument does not have the \texttt{TARGET} or
    \texttt{POINTER} attribute, any pointers associated with the actual
    argument do not become associated with the corresponding dummy
    argument on invocation of the procedure.
  
    If the dummy argument has the \texttt{TARGET} attribute and the
    corresponding actual argument has the \texttt{TARGET} attribute but
    is not an array section with a vector subscript:
    \begin{enumerate}
    \item Any pointers associated with the actual argument become
      associated with the corresponding dummy argument on invocation of
      the procedure.
  
    \item When execution of the procedure completes, any pointers
      associated with the dummy argument remain associated with the actual
      argument.
    \end{enumerate}

    If the dummy argument has the \texttt{TARGET} attribute and the
    corresponding actual argument does not have the \texttt{TARGET}
    attribute or is an array section with a vector subscript, any pointers
    associated with the dummy argument become undefined when execution of
    the procedure completes.
  \end{quote}
\end{rationale}

\subsection{Example}

Here is an example that illustrates the restrictions of this section:

\CODE

      INTEGER, TARGET, DIMENSION (10) :: ACT
      INTEGER, POINTER, DIMENSON (:) :: POINTS_TO_ACT, POINTS_TO_DUM
!HPF$ DISTRIBUTE ACT(BLOCK)

      POINTS_TO_ACT => ACT
      CALL F(ACT)
      POINTS_TO_DUM(1) = 1             ! ILLEGAL

      CONTAINS
        SUBROUTINE F(DUM)
          INTEGER, TARGET, DIMENSION(10) :: DUM
        !HPF$ DISTRIBUTE DUM(CYCLIC)

          POINTS_TO_DUM => DUM
          POINTS_TO_ACT(1) = 1         ! ILLEGAL
        END SUBROUTINE
      END

\EDOC

The assignment to \texttt{POINTS_TO_DUM(1)} is illegal because it
violates item~\ref{first-item}; the assignment to
\texttt{POINTS_TO_ACT(1)} is illegal because it violates
item~\ref{second-item}.

\section{Argument Passing and Sequence Association}

For actual arguments in a procedure call, Fortran allows an array
element (scalar) to be associated with a dummy argument that is an
array.  It furthermore allows the shape of a dummy argument to differ
from the shape of the corresponding actual array argument, in effect
reshaping the actual argument via the procedure call.  Storage
sequence properties of Fortran are used to identify the values of the
dummy argument.  This feature, carried over from FORTRAN 77, has been
widely used to pass starting addresses of subarrays, rows or columns
of a larger array, to procedures.  For HPF arrays that are potentially
mapped across processors, this feature is not fully supported.


\subsection{Sequence Association Rules}

\begin{enumerate}
  
\item When an array element or the name of an assumed-size array is
  used as an actual argument, the associated dummy argument must be a
  scalar or specified to be a sequential array.
  
  An array-element designator of a nonsequential array must not be
  associated with a dummy array argument.
  
\item When an actual argument is an array or array section and the
  corresponding dummy argument differs from the actual argument in
  shape, then the dummy argument must be declared sequential and the
  actual array argument must be sequential.
  
\item An object of type character (scalar or array) is nonsequential
  if it conforms to the requirements of Definition~\ref{seq-var} of
  Section~\ref{sequence-defs}.  If the length of an explicit-length
  character dummy argument differs from the length of the actual
  argument, then both the actual and dummy arguments must be
  sequential.

  
\item Without an explicit interface, a sequential actual may not be
  associated with a nonsequential dummy and a nonsequential actual may
  not be associated with a sequential dummy.  (This item merely
  repeats part of Section~\ref{mapsub:ExplicitInterfaces}


\end{enumerate}


\subsection{Discussion of Sequence Association}

When the shape of the dummy array argument and its associated actual
array argument differ, the actual argument must not be an expression.
There is no HPF mechanism for declaring that the value of an
array-valued expression is sequential.  In order to associate such an
expression as an actual argument with a dummy argument of different
rank, the actual argument must first be assigned to a named array
variable that is forced to be sequential according to
Definition~\ref{seq-var} of Section~\ref{sequence-defs}.

\subsection{Examples of Sequence Association}

Given the following subroutine fragment:
                                                                \CODE
      SUBROUTINE HOME (X)
      DIMENSION X (20,10)
                                                                \EDOC
By rule 1
                                                                \CODE
      CALL HOME (ET (2,1))
                                                                \EDOC
is legal only if \texttt{X} is declared sequential in \texttt{HOME}
and \texttt{ET} is sequential in the calling procedure.

Likewise, by rule 2 and 4
                                                                \CODE
      CALL HOME (ET)
                                                                \EDOC
requires either that \texttt{ET} and \texttt{X} are both sequential arrays or 
that \texttt{ET} and \texttt{X} have the same shape and have the same
sequence attribute.


Rule 3 addresses a special consideration for  objects of type 
character. Change of the length of character objects across 
a call, as in

                                                                \CODE
      CHARACTER (LEN=44) one_long_word
      one_long_word = 'Chargoggagoggmanchaugagoggchaubunagungamaugg'
      CALL webster(one_long_word)

      SUBROUTINE webster(short_dictionary)
      CHARACTER (LEN=4) short_dictionary (11)
          !Note that short_dictionary(3) is 'agog', for example
                                                                \EDOC

\noindent
is conceptually legal in Fortran. In HPF, both the actual argument and
dummy argument must be sequential.
(Chargoggagoggmanchaugagoggchaubunagungamaugg is the original Nipmuc
name for what is now called Lake Webster in Massachusetts.)
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% File: spmd-to-hpf-ext.tex

% Contents:
% Approved Extension for SPMD interface to HPF  for HPF 2.0 document

% Revision history:
% Aug-8-96	Created by Scott B. Baden, UCSD
% Aug-15-96	Scott B. Baden, UCSD


\chapter{Approved Extensions for SPMD calling HPF}
\label{ch-spmd-hpf}

{\em
Comments on this chapter should be directed to 
Scott Baden ({\tt baden@cs.ucsd.edu})
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on SPMD-to-HPF}'' as the {\tt Subject:}
line.
\par
}


\section{SPMD calling HPF}
\label{f90-locals}

\newcommand{\PROCS}  {{\tt PROCESSORS} }
\newcommand{\HPFINIT}  {{\tt HPF\_INIT} }
\newcommand{\HPFLOCAL}  {{\tt EXTRINSIC(HPF\_LOCAL)}}
\newcommand{\MAD}  {{\tt MAD}}
\newcommand{\CPP}  {{\tt C++}}
\newcommand{\MA}  {{\tt MAPPED\_ARRAY}}
\newcommand{\TMA}  {{\tt TO\_MAPPED\_ARRAY}}
\newcommand{\offset}[1]{\begin{center} \tt #1 \end{center}} 

% ******************** Start of Document ********************

\section{SPMD Coordination of HPF}

The current HPF standard does not address the problem of
coordinating the concurrent execution of multiple HPF
procedure invocations, nor their interaction via
an SPMD harness written in an extrinsic language such as \CPP.
We propose an interface for
coordinating concurrently executing HPF procedures from an extrinsic SPMD layer.
This interface requires neither language extensions nor new language
features, and requires only a handful of library entries
that access the HPF run time system.
The proposed interface is language-independent.  It enables
inter-operability between software components developed in different
languages.

Note: Chuck Koelbel and Joel Saltz assisted in the development of this
proposal.


\section{Programming Model}
Our model comprises multiple HPF invocations that interact
with each other concurrently.
Separate HPF invocations will be orchestrated
via an  SMPD program, and
may or may not involve the identical code.
HPF invocations will import scalars and global arrays allocated from 
the SMPD  program.
The primary concern here in how to
deal with global arrays.

The SPMD code which controls the
interaction of multiple HPF invocations
may be   written in \HPFLOCAL\ or another
extrinsic language, e.g. \CPP.  We will use \HPFLOCAL\ here.
Other possibilities include multiple HPF programs that communicate
by calling an extrinsic SPMD program, but this has already been
addressed elsewhere in this document (see {\em An HPF binding for MPI},
chapter \ref{HPF-binding-for-MPI}.)
The discussions in this approved
extension augment those outlined in the \HPFLOCAL\ interface with extensions
that may facilitate coordination via extrinsic languages like \CPP.


\section{The Interface}
Our proposed interface
specifies the interaction of an SPMD program, written
in an extrinsic language,  that calls HPF.
The interface supports the allocation of, and access to,
HPF global arrays from the SPMD coordinating code.
SPMD code views
each HPF global array as an entity called
a {\em mapped array} which will refer to as a \MA.

It is assumed that the HPF compiler translates a call to an HPF
entry as follows.  First, an implementation-specific {\em name-mangling}
rule is applied to the entry name to conform with linkage conventions.
Second, each global array argument is converted to a \MA\
argument.  (Scalars are passed unchanged.)
The conversion process in implementation-dependent.
For example, some implementations convert each global array argument
into a pair of arguments: a
{\em mapped array descriptor} or \MAD\, and a pointer to
the start of the local storage for the mapped array.  In this case two
arguments would actually be passed for each mapped array argument,
though the number and representation of these arguments is generally
implementation-dependent.

By an abuse of notation we will refer to a mapped array reference
as if it were a reference to value of a distinguished type \MA.
While no such type may in fact  exist, the notation simplifies the
ensuing discussions.
We will employ the notation \TMA{\tt (A)} to
designate the desired conversion of global array argument {\tt A}
to a reference of type \MA.
Thus, an argument of the form 
\TMA{\tt (A)}
is understood to represent the \(k>1\) actual parameters, which
might, for example,
contain a corresponding \MAD\ and starting address.
Similarly a declaration of the form
\offset{MAPPED\_ARRAY(A)} is understood to
declare \(k>1\) variables;  in the above example, there would
be one declaration for the \MAD,
another for the starting address to the corresponding local data.


As described below,
the interface includes various
entries for querying and manipulation \MA.
This interface should be packaged as a module
(in the case of \HPFLOCAL) as described at the end of this chapter.
This module must be {\tt USEd} in all program source files
that employ the proposed interface.

\subsection{Execution Model}

This proposal defines a  language-independent
interface consisting of a set of
entries that enables SPMD code
written in an extrinsic language to communicate with HPF.
Interfaces for  other extrinsic languages,
e.g. C are out of the scope of this document; refer to
section \ref{interoperability-with-c} which discusses
the symmetric case of calling C from HPF.

We define SPMD execution as follows.  An SPMD program
executes on a {\em process group}.
We identify
an HPF \PROCS\  arrangement with  a process group, and employ
an opaque object called 
a {\em communicator} (as in MPI) to  specify the  group's membership.
The advantage of this approach is that the values returned by
{\tt NUMBER\_OF\_PROCESSORS} and {\tt PROCESSORS\_SHAPE} are well-defined,
as are collective communication operations.
%Note that it is possible to dynamically change the members of a process
%group or to change the group's topology by modifying
%attributes of the
%communicator.
Each process will be considered a physical processor by the HPF code.  The
called HPF program will have access to members of the process group.
It will not, however, have direct
access to processes outside that group.

All members
of a process group execute the same program in loosely synchronous
fashion, collectively 
making calls to HPF procedures (including those defined by
the proposed interface)
{\em as if\ } at the same time.
(Calls to HPF from SPMD may or may not need to be explicitly synchronized
at a barrier.)
As far as the HPF procedure is concerned, it will
not know
the origin of the argument, which could have in fact originated from
another HPF program.  It follows that
the SPMD program is responsible for passing mapped arrays to an HPF
procedure in conformance  with the procedure's expectations, i.e. the distribution
must match and so on. All invocations of HPF procedures
in the process group must pass the same \MA\ in each corresponding position
of the argument list (remembering that the accompanying local data
will be generally be different for each invocation.)
Scalar arguments must be consistent among
all members of the process group.


\begin{implementors}
Implementation of the ``HPF-from-extrinsic'' interface will be
facilitated with MPI.
However, implementors are free
to  employ their own implementation strategy.
Implementors who do not employ MPI 
need a mechanism for defining groups of processors that
only talk to each other; non-MPI implementations will obviously treat
these
differently from MPI ones.

The use of the proposed interface will be simplified by the provision
of a macro called \TMA, to
translate an HPF
global array reference to a \MA, containing the appropriately formed
\MAD\ and the start of the local data area.
\end{implementors}

\subsection{HPF Run Time Initialization}

A call to a procedure \HPFINIT\ is required to establish
various state needed by the HPF run time system, that will, for
example, enable,
the processor to determine `who it is.'
\HPFINIT\ must   be passed a communicator corresponding
to the process group used to invoke the HPF program(s).
Successive calls to \HPFINIT\ may be used to set up alternative
\PROCS\ topologies or as required to invoke HPF code
on different processor groups.

\begin{implementors}
\HPFINIT\ should extract the \PROCS\ topology from the communicator
passed into it.

A mechanism is required for managing MPI-style communicators;
either MPI will be available from the SPMD program, or the
implementor must provide equivalent functionality.
\end{implementors}

Two or more HPF invocations may be simultaneously active if they execute on
different communicators with disjoint process groups.
To achieve this, the individual groups each define their own communicator.
The separate communicators are then used by \HPFINIT\
to establish the communication domains.

To handle multiple HPF invocations across different
processing groups, the SPMD coordinating code  may need to
explicitly query each processor  for membership within the desired communicator.
For example, if we are invoking procedures {\tt A1, A2}
on one processor group, and procedure {\tt B} on another, then
we employ the following:
\begin{verbatim}
!     Set up the processor groups
      call HPF_INIT(GroupA, ...)
      call HPF_INIT(GroupB, ...)

!     isMember( ) determines membership within the respective communicators
      if ( isMember(GroupA)) then
          call A1(...)      
          call A2(...)
      else if ( isMember(GroupB)) then
          call B(....)     
      end if
\end{verbatim}


HPF programs associated with overlapping communicators can also be defined,
but require additional system support to execute in parallel.  (In effect,
the underlying system must allow multi-threading to allow the process(es) in
the overlap to participate in both HPF programs at once.)  Such support may
be desirable, but is not mandated by this proposal.
Overlapping communicators could, however, be useful in different phases.
For example, one phase might use 8 processes, followed by another phase
using only 4.  The programmer could accomplish this by creating an
8-process communicator and a 4-processes communicator with a subset of the
processes.  \HPFINIT\ would have to be called to establish
the communicator for each phase to alert
the HPF runtime that a different communicator was in use.

Regardless of how the communicators are set up, an HPF procedure has
access only to the process group associated with the communicator in the
last executed \HPFINIT\ call.
This allows us to define {\tt NUMBER\_OF\_PROCESSORS} to return the number
of processes in that communicator, and similarly make consistent
definitions for the other HPF inquiry procedures.
It follows that
SPMD code must invoke an HPF procedure on {\em exactly}
those processors in the intended processor group---no more an no less.
This will likely be supported by a conditional statement which
will determine membership within the respective communication domains
established by SPMD program.

Note that physical processors in different communicators may
return different values for {\tt NUMBER\_OF\_PROCESSORS}, but they cannot
be executing the same instantiation of an HPF procedure.
This implies that
actual arguments to an HPF procedure must all be allocated
from the same process group,
and that data motion between mapped arrays allocated to different
process groups must be handled at the SPMD level.
(MPI's inter-communicators allow precisely
this sort of communication.)
We restrict global data accessed in the HPF procedure
in the same way.


\subsection{Global Array Allocation From SPMD}

The functionality required to support extrinsic SPMD coordination of HPF
invocations centers on the ability to allocate, from the SPMD level, global
HPF arrays with a specified \PROCS\ arrangement, alignment,
and decomposition.  In the interest of simplicity, allocation
will be restricted as follows.
\begin{enumerate}
\item Only arrays of built types are permitted, i.e. arrays
of derived types are excluded.

\item Only {\tt BLOCK, *, CYCLIC, } and {\tt CYCLIC(N)}
decompositions are supported.

\item Only the  identity alignment is supported.  Identically
aligned arrays must have the same rank and extents.
\end{enumerate}


A process group dynamically allocates a mapped array using the call

\noindent
\subsubsection*{alloc\_mapped\_arrayTTT(A, NDIM, EXTENTS, DECOMP, [ALIGN])}

\begin{tabular}{ll}
{\bf OUT} A &         a MAPPED\_ARRAY \\
{\bf IN} NDIM & number of dimensions \\
{\bf IN} EXTENTS & extents of the indices of the array  ({\tt 2*NDIM} entries) \\
{\bf IN} DECOMP & decomposition ({\tt NDIM} entries) \\
{\bf IN} ALIGN & a previously allocated \MA\ (optional) \\
\end{tabular}
\vspace{0.1in}


\noindent
{\tt TTT} is one of 5 built in HPF types:
\offset{REAL, DOUBLE PRECISION, COMPLEX, DOUBLE PRECISION COMPLEX, INTEGER.}

The first
argument actually refers to the global array to be allocated by HPF.
The {\tt NDIM} and {\tt EXTENT} arguments
specify the number  and extent of the array axes, the {\tt DECOMP}
argument their decomposition across processors.  Each element
of {\tt DECOMP}  must be one of the following predefined names:
\offset{SERIAL, BLOCK, CYCLIC, CYCLIC(N)}

\noindent
where {\tt CYCLIC(N)} will be mapped onto distinct values for 
distinct values of {\tt N.}

The final argument is optional; it is specifies an existing array
to which the newly-allocated array will be aligned.
Such allocations are restricted to identity alignments only;
the {\tt NDIM, EXTENTS,} and {\tt DECOMP} specifications must
also be identical as well.




The extrinsic SPMD layer may access a global array through a
\MA\ reference.
The interface  does not permit direct access
to the \MA, since manufacturers need flexibility in representing a mapped
array.
Rather, we treat a \MA\ as an opaque object, and provide
entries that
permit the SPMD program to query
the global array---e.g.
determine global shape, local shape, decomposition, and so on---or
to modify it.
This is nicely defined in the
\HPFLOCAL\ interface (see \ref{hpf-local}),
which we adapt for the task at hand.

\begin{enumerate}
\item All mapped HPF arrays accessible from an SPMD procedure are logically carved
up into blocks; the SPMD process executing on a particular physical
processor sees an array containing just those elements of the global
array that are mapped to that physical processor.

\item The model assumes that array axes are mapped independently to axes of a
rectangular \PROCS\ grid, each array axis to at most one \PROCS\
axis (no ``skew" distributions) and no two array axes to the same
\PROCS\ axis.  This restriction suffices to ensure that each
physical processor contains a subset of array elements that can be
locally arranged in a rectangular configuration (of course to compute
the global indices of an element given its local indices or vice verse,
may be quite a tangled computation-- but it will be possible)



\item
The portion of a mapped array argument
in an {\tt HPF\_LOCAL} subprogram
associated with a global array dummy argument  in an HPF program
may be accessed in a block-by-block
fashion.  Library procedures (described below) such as {\tt LOCAL\_BLKCNT},
{\tt
LOCAL\_LINDEX}, and {\tt LOCAL\_UINDEX}, allow easy access to the local
storage of a particular block.
\end{enumerate}

\begin{implementors}
Random access to the elements of a mapped array is likely to be
expensive, but aggregate (block) moves  should be efficient.


Implementations that employ ghost cells or shadow regions may need to provide
the capability of accessing such additional data.  This proposal
does not specify how ghost cells are to be accessed or manipulated.
\end{implementors}



\subsection{Queries and Mapped Array Access}

We require a number of entries to enable
the programmer to access and query a mapped array from SPMD.
These queries are divided into pre-existing functionality,
derived from the \HPFLOCAL\ specification,
as well as {\em new} functionality.



\subsubsection{Existing functionality}
Included are\\

\begin{tabular}{lll}
{\tt GLOBAL\_ALIGNMENT} & {\tt GLOBAL\_DISTRIBUTION} & {\tt GLOBAL\_TEMPLATE } \\
{\tt GLOBAL\_LBOUND  } & {\tt GLOBAL\_UBOUND } & {\tt GLOBAL\_SHAPE  }\\
{\tt GLOBAL\_SIZE } & {\tt ABSTRACT\_TO\_PHYSICAL  } & {\tt PHYSICAL\_TO\_ABSTRACT }\\
{\tt LOCAL\_TO\_GLOBAL  } & {\tt GLOBAL\_TO\_LOCAL } & {\tt LOCAL\_BLKCNT  }\\
{\tt LOCAL\_LINDEX } & {\tt LOCAL\_UINDEX} & {\tt MY\_PROCESSOR }\\
\end{tabular}

\ \\
\noindent
Note that we employ a \MA\ reference
in lieu of the
global HPF array arguments that the \HPFLOCAL\ interface
specifies for these functions.
For example, we consider the procedure {\tt GLOBAL\_SHAPE}
(Other procedures will be
handled similarly):

% Definition of GLOBAL_SHAPE
\subsubsection*{GLOBAL_SHAPE(SOURCE)}

\? Description.	Returns the shape of the global HPF array associated
	with \MA\ passed as the actual argument.  \\

\? Class.  Inquiry function.	\\

\? Argument.

\Arg SOURCE			A \MA.  \\

\? Result Type, Type Parameter and Shape.  The result is a default integer
                                array of rank one whose size is equal to the
                                rank of the HPF global array associated
				with {\tt SOURCE}.  \\

\? Result Value.         The value of the result is the shape of the global
                         array associated with the actual argument
                         associated with {\tt SOURCE}.  \\

\? Examples.             Assuming that global array {\tt A} has been allocated by the call\\
			  {\tt alloc\_mapped\_array(TO\_MAPPED\_ARRAY(A),NDIM=2,EXTENTS=/(3,100,1,200/),...),}
			  the value returned by
                         {\tt GLOBAL_SHAPE(TO\_MAPPED\_ARRAY(A))} is \VECTOR{98 200}.
\\

\begin{implementors}
Since HPF procedures can't distinguish the difference between a
global argument passed from an explicit SPMD program
and an HPF program,
it would be possible to implement the above functions  using
the \HPFLOCAL\ interface.
However, doing so  may not to
be as efficient as taking advantage of direct access to
layout information provided by the compiler.
\end{implementors}

\subsubsection{New Functionality}
In addition to the procedure for allocating global arrays,
we need a procedure to copy
one mapped array into another.
The calling sequence of this operation is as follows:

\subsubsection*{copy\_mapped\_array\_TTT(SRC, DEST)}

\begin{tabular}{r ll}
{\tt IN} & {\tt SRC} &		\MA -- source \\
{\tt OUT} & {\tt DEST} &	\MA -- destination \\
\end{tabular}

\noindent
where {\tt TTT} is one of 5 built in HPF types:
\offset{REAL, DOUBLE PRECISION, COMPLEX, DOUBLE PRECISION COMPLEX, INTEGER.}

\noindent
The source and destination descriptors may or may not  be allocated to the same
processor group.

There is also  a variant of
{\tt copy\_mapped\_arrayTTT} that copies over designated array
sections:


\subsubsection*{copy\_mapped\_array\_secTTT(SRC, DEST, S\_SECT, D\_SECT)}

\begin{tabular}{r ll}
{\tt IN} & {\tt SRC} &		\MA -- source \\
{\tt OUT} & {\tt  DEST} &		\MA -- destination  \\
{\tt IN} & {\tt S\_SECT} &		source array section specifier \\
{\tt IN} & {\tt D\_SECT} &		destination array section specifier \\
\end{tabular}

The array section specifiers are {\tt INTEGER} \(d\)-tuples
(arrays)
where \(d\) is the common rank of the arrays.
The format of these tuples is \((r_0, r_1, ..., r_{d-1}\))
where each \(r_k\) specifies the integer range of indices for axis \(k\),
i.e. the array section {\tt (3:4, 5:6)} is specified as
{\tt /(3,4, 5,6/).}


\begin{implementors}
Though the {\tt copy\_mapped\_array\_secTTT( )}
could be implemented
using the \HPFLOCAL\ interface, doing so may not to
be as efficient as taking advantage of direct access to
layout information provided by the compiler.
\end{implementors}


\subsection{Summary of what is to be provided}
In practice, multi-lingual programming  can be given only minimal
language and compiler support.
Some installation-dependent coding is
required, for example to handle name mangling, argument
passing conventions, and so on.  Such code is generally not portable.

We propose an interface that does not rely on language extensions,
yet which offers reasonable assurances of portability.
To this end,
we strongly recommend that sites wishing to support SPMD applications
inter-operating with
HPF provide the following constants and entries and package
them in a 
{\tt MODULE}.  (In the
case of {\tt f77, C,} or \CPP, these would be packaged as part of
a header file, and probably contain a class definition in the case of \CPP.)
In addition, macros should be defined (described below) to facilitate
manipulation of a \MA.

\subsubsection*{Constants}
\begin{tabular}{llll}
{\tt SERIAL} & {\tt BLOCK} & {\tt CYCLIC} & {\tt CYCLIC(K)}\\
\end{tabular}

Note: {\tt CYCLIC(K)} will probably be supported with a macro.

\subsubsection*{Required Entries}
\begin{tabular}{ll}
{\tt HPF_INIT} & {\tt alloc\_mapped\_arrayTTT}\\
{\tt copy\_mapped\_array\_TTT} & {\tt copy\_mapped\_array\_secTTT} \\
\end{tabular}

\vspace{0.1in}
\noindent
Note: {\tt TTT} is one of 5 built in HPF types:
\offset{REAL, DOUBLE PRECISION, COMPLEX, DOUBLE PRECISION COMPLEX, INTEGER.}


\noindent
The following entries are optional, since they can 
be supported by \HPFLOCAL:\\

\begin{tabular}{lll}
{\tt GLOBAL\_ALIGNMENT} & {\tt GLOBAL\_DISTRIBUTION} & {\tt GLOBAL\_TEMPLATE } \\
{\tt GLOBAL\_LBOUND  } & {\tt GLOBAL\_UBOUND } & {\tt GLOBAL\_SHAPE  }\\
{\tt GLOBAL\_SIZE } & {\tt ABSTRACT\_TO\_PHYSICAL  } & {\tt PHYSICAL\_TO\_ABSTRACT }\\
{\tt LOCAL\_TO\_GLOBAL  } & {\tt GLOBAL\_TO\_LOCAL } & {\tt LOCAL\_BLKCNT  }\\
{\tt LOCAL\_LINDEX } & {\tt LOCAL\_UINDEX} & {\tt MY\_PROCESSOR }\\
\end{tabular}

\vspace{0.1in}
As previously noted,
this approach
may not to
be as efficient as having direct access to
layout information provided by the compiler, but it will expedite
an initial prototype.

\subsubsection*{Optional Macros}
It is recommended that the macro
\TMA\ be provided to facilitate the handling of the multiplicity
of  values that comprise a \MA\ argument.
Similarly, the macro \MA\  is recommended for declaring a value of 
type \MA, e.g.
\offset{MAPPED\_ARRAY(A)}
declares a set of variables that collectively represent
a \MA.
\section{Programming Example}


The application is to iteratively solve Poisson's equation on a
2-dimensional irregularly-shaped domain consisting of two coupled rectangular
blocks of different sizes.  The same solver is applied to each  block.  


Because the blocks have different sizes we will
allocate them to different size \PROCS\ subsets in order to balance
the workloads.  Prior to computing,
each block must furnish boundary conditions that couple
it to the other block.


\CODE
! Example illustrating coordination from an extrinsic layer
! Solve the Laplace Equation on an irregular domain using Red/Black SOR
! The computational domain consists of two squares A&B
! sitting side by side and aligned with the y axis
! Square A is m x m, Square B is n x n

extrinsic(hpf_local) program iter
!   The MAPPED_ARRAY package is part of the interface
!   It includes definitions for constants like BLOCK, SERIAL,
!   the various routines that allocate global arrays, and so on
    use MAPPED_ARRAY
!   This package specifies an HPF binding for MPI
    use MPI

!   MAPPED_ARRAY() is a macro which declares the various pieces of information
!   that make up a MAPPED_ARRAY
    MAPPED_ARRAY(A)
    MAPPED_ARRAY(B)

!   Extents of A and B
    integer, array(4) :: A_EXT = /(0,m+1,0,m+1/), B_EXT = /(0,n+1,0,n+1/)
!   Their decomposition: SERIAL corresponds to  * in HPF
    integer, array(2) :: DECOMP = /(BLOCK,SERIAL/)

    real resid, convergence
    real function smooth
    real, parameter :: EPSILON = 0.001

! Communicators
    Communicator COMM_A, COMM_B
   
!   The size of the blocks are inputs to the program
    read *, m, n

!   Allocate processors 0 to K-1  to block A, the remainder to block B
!   The value of K is determined by the relative sizes of m & n
!   ZERO_TO_KM1 and K_TO_PM1 are integer "color" arrays (i.e.  MPI)
!   specifying the  membership of each processor in the respective groups

!   Set up the process groups and communicators, one for each block
    call MPI_COMM_SPLIT(MPI_COMM_WORLD,ZERO_TO_KM1,DUMMY,COMM_A,IERROR)
    call init_HPF(COMM_A)

    call MPI_COMM_SPLIT(MPI_COMM_WORLD,K_TO_PM1,DUMMY,COMM_B,IERROR)
    call init_HPF(COMM_B)

    if (isMember(COMM_A)
!       TO_MAPPED_ARRAY( ) converts the global array reference to a
!       MAPPED_ARRAY.  k>1 arguments may correspond to TO_MAPPED_ARRAY(A)
        call alloc_mapped_arrayREAL(TO_MAPPED_ARRAY(A), 2, A_EXT, DECOMP)
    if (isMember(COMM_B)
        call alloc_mapped_arrayREAL(TO_MAPPED_ARRAY(B), 2, B_EXT, DECOMP)

    convergence = 10.0 * epsilon

    do while ( convergence < epsilon )
!       Fill in the boundary cells
        mn = min(m,n)
        I0 = /(m+1,m+1,1,mn/)
        I1 = /(m,m,1,mn/)

!       All processors in COMM_A and COMM_B must participate
!       which in this case covers all processors in MPI_COMM_WORLD
!       In a multiblock code with > 2 blocks, appropriate guards would be
!       required to restrict execution of copy_mapped_array_secTTT( ), as
!       2 communicating grids would cover only a subset of MPI_COMM_WORLD

        call copy_mapped_array_secREAL(MAPPED_ARRAY(B),MAPPED_ARRAY(A),I0,I0)
        call copy_mapped_array_secREAL(MAPPED_ARRAY(B),MAPPED_ARRAY(A),I1,I1)

!       Ensures that the global reductions are done correctly.
        residA = 0
        residB = 0

!       These calls to HPF execute in different processor groups; their
!       respective arguments were allocated with different communicators
        if (isMember(COMM_A))
            residA = smooth(A)

        if (isMember(COMM_B))
            residB = smooth(B)

!       global reduction over all processes (MPI functionality)
        call _max_scalar_REAL(residA, MPI_COMM_WORLD)
        call _max_scalar_REAL(residB, MPI_COMM_WORLD)

        convergence = amax(residA, residB)
    enddo
end program

\EDOC
\end{document}
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From owner-hpff-doc  Tue Aug 20 10:29:58 1996
Received: (from daemon@localhost) by cs.rice.edu (8.7.1/8.7.1) id KAA27025 for hpff-doc-out; Tue, 20 Aug 1996 10:29:58 -0500 (CDT)
Date: Tue, 20 Aug 1996 10:29:58 -0500 (CDT)
From: owner-hpff-doc
Message-Id: <199608201529.KAA27025@cs.rice.edu>
Subject: hpff-doc: Next Draft HPF2 document
>From: Mary E Zosel <zosel@llnl.gov>
Sender: owner-hpff-doc
Precedence: bulk

---------------------------------------------------------------------------
hpff-doc@cs.rice.edu is a mailing list for HPF 2.0 language specification
authors and editors.  Instructions for adding or deleting yourself from this
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Hmmm - there seem to be a collection of minor computer problems
both here, at Rice, and in my typing conspiring to keep this document
from going out.

Following find the current version of the HPF2 document ... it is
uuencoded, compressed, tar file.  When you decode it, I messed up
the uuencode line and it comes out as uu817 rather than an
appropriately named .Z file so you will have to rename to uncompress.

Find a README in the file for the current status.  We will cut a new
version right after labor day.

PLEASE all "readers" - make a careful effort to look over the chapter
you signed up for.  If it is good shape, then look for "little details" -
if it is still pretty much in draft stage, you might volunteer some
help.

   -mary-

====================
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MQ!L,$RKPR(3)NW-=(4M=][-BUQWBBEUE`'@=<$U>YULST=WK3FROJU4>OV[-
()]2C:!'Y0`#)
`
end

--UAA14923.840513073/coral.llnl.gov--


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From owner-hpff-doc  Tue Aug 20 12:58:56 1996
Received: (from daemon@localhost) by cs.rice.edu (8.7.1/8.7.1) id MAA02824 for hpff-doc-out; Tue, 20 Aug 1996 12:58:56 -0500 (CDT)
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Date: Tue, 20 Aug 1996 13:01:06 -0500
To: hpff-doc, hpff-core
From: chk@cs.rice.edu (Chuck Koelbel)
Subject: hpff-doc: Re: Next Draft HPF2 document
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OK, the Rice problems seem to be ameliorating.  (Except for demands on
Chuck's time, which are getting worse...)

Anyway, there is a new, improved distribution of the HPF 2.0 document.
You can pick it up at ftp://titan.cs.rice.edu/public/HPFF/hpf2.0-draft/
        If you want one (or a few) TeX files, they are in that directory
        If you want the whole enchilada, go from there to
        Releases/20-aug-96.tar.gz for a gzipped tar file

Two minor changes from Mary's version:

* I fixed the \ith problem (a missing macro in syntax-macs.tex), so there
should be no TeX errors.  Lots of warnings, though!

* I added skeletal instructions for running latex to the README file.

Happy proofreading...

                                                Chuck

At 10:29 08/20/96, owner-hpff-doc wrote:
>Hmmm - there seem to be a collection of minor computer problems
>both here, at Rice, and in my typing conspiring to keep this document
>from going out.
>
>Following find the current version of the HPF2 document ... it is
>uuencoded, compressed, tar file.  When you decode it, I messed up
>the uuencode line and it comes out as uu817 rather than an
>appropriately named .Z file so you will have to rename to uncompress.
>
>Find a README in the file for the current status.  We will cut a new
>version right after labor day.
>
>PLEASE all "readers" - make a careful effort to look over the chapter
>you signed up for.  If it is good shape, then look for "little details" -
>if it is still pretty much in draft stage, you might volunteer some
>
>...


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From owner-hpff-doc  Tue Aug 20 13:20:20 1996
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Date: Tue, 20 Aug 1996 13:01:06 -0500
To: hpff-doc, hpff-core
From: chk@cs.rice.edu (Chuck Koelbel)
Subject: hpff-doc: Re: Next Draft HPF2 document
Sender: owner-hpff-doc
Precedence: bulk

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OK, the Rice problems seem to be ameliorating.  (Except for demands on
Chuck's time, which are getting worse...)

Anyway, there is a new, improved distribution of the HPF 2.0 document.
You can pick it up at ftp://titan.cs.rice.edu/public/HPFF/hpf2.0-draft/
        If you want one (or a few) TeX files, they are in that directory
        If you want the whole enchilada, go from there to
        Releases/20-aug-96.tar.gz for a gzipped tar file

Two minor changes from Mary's version:

* I fixed the \ith problem (a missing macro in syntax-macs.tex), so there
should be no TeX errors.  Lots of warnings, though!

* I added skeletal instructions for running latex to the README file.

Happy proofreading...

                                                Chuck

At 10:29 08/20/96, owner-hpff-doc wrote:
>Hmmm - there seem to be a collection of minor computer problems
>both here, at Rice, and in my typing conspiring to keep this document
>from going out.
>
>Following find the current version of the HPF2 document ... it is
>uuencoded, compressed, tar file.  When you decode it, I messed up
>the uuencode line and it comes out as uu817 rather than an
>appropriately named .Z file so you will have to rename to uncompress.
>
>Find a README in the file for the current status.  We will cut a new
>version right after labor day.
>
>PLEASE all "readers" - make a careful effort to look over the chapter
>you signed up for.  If it is good shape, then look for "little details" -
>if it is still pretty much in draft stage, you might volunteer some
>
>...


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From owner-hpff-doc  Thu Aug 29 07:33:22 1996
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	id LAA14005; Thu, 29 Aug 1996 11:59:17 +0100
From: Mike Delves <delves@nasoftwr.demon.co.uk>
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	id AA07820; Thu, 29 Aug 96 11:57:47 BST
Local-From: delves@ferrari (Mike Delves)
Message-Id: <9608291057.AA07820@ferrari.nasoftware>
Subject: hpff-doc: Comments on Library
To: Rob Schreiber <schreiber@hpl.hp.com>, HPF Documents <hpff-doc@cs.rice.edu>
Date: Thu, 29 Aug 1996 11:57:46 +0100 (BST)
Cc: Dave Watson NAS <dave@nasoftwr.demon.co.uk>
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Dear Dr Schreiber,

We have the following comments/queries on the Intrinsic
and Library Procedures chapter:

1) It is not clear to us why ILEN is an intrinsic while POPCNT,
LEADZ, POPPAR are library functions. All are on the same level.
Further, if ILEN is intrinsic it may appear in specification
expressions - causing trouble for a "compiler" which actually is a
source to source translator to Fortran.

2) For many library routines the "major" argument <may be of any type>.
Taken literally (as it should be) this includes derived types. 

a) Is this intended (our guess is not: else many troubles ensue).
b) If not, the wording should make this clear: <any intrinsic type>

3) For many other arguments (eg INDX1,.. and MASK of COPY_SCATTER)
the type INTEGER or LOGICAL is specified. Our guess is that this
is meant to mean <default integer> and <default logical>. Is this
the intention? If so, the wording should be tightened.

My apologies if these comments have been made many times before.

Best wishes

Mike Delves


-- 
------------------------------------------------
Mike Delves                |Tel: +44 151 709 4738
N.A Software Ltd           |Fax: +44 151 709 5645
Roscoe House, 62 Roscoe St |delves@nasoftwr.demon.co.uk
Liverpool L1 9DW, UK       |http://www.nasoftware.co.uk/home.html
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From owner-hpff-doc  Thu Aug 29 15:51:19 1996
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Message-Id: <199608292051.PAA21714@cs.rice.edu>
From: Jaspal.Subhlok@N2.SP.CS.CMU.EDU
Subject: hpff-doc: Task region changes in parallel-ext.tex
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[I just realized that the task region changes have not propagated to the
 current draft. I am resending the corresponding chapter with the changes
 i.e. current text from the ftp site + new TASK_REGION section. We should
 probably place this on the ftp site and then update it with new ON  and
 RESIDENT sections when they are ready. -- jas]



% File: parallel-ext.tex

% Contents:
% Approved Extensions for data-parallel computation for HPF 2.0
% document, including
%       ON
%       TASK
%       RESIDENT

% Revision history:
% May-10-96     Created by Charles Koelbel, Rice University
%               (from HPF 2.0 proposals)
% Aug-27-96     Expanded section on task parallelism added
%               Jaspal Subhlok


\chapter{Approved Extensions for Data and Task Parallelism}
\label{ch-parallel-ext}

{\em
Comments on this chpater should be directed to 
Chuck Koelbel ({\tt chk@cs.rice.edu}),
Jaspal Subhlok ({\tt jass@cs.cmu.edu}),
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on Extended Parallelism}'' as the {\tt Subject:}
line.
\par
}


There are three major Approved Extensions related to parallel
execution:
\begin{enumerate}
\item The {\tt ON} directive, which partitions computations among the
processors of a parallel machine (much as the {\tt DISTRIBUTE}
directive partitions the data among the processors).
\item The {\tt RESIDENT} directive, which asserts that certain data
accesses do not require interprocessor data movement for their
implementation.
\item The {\tt TASKING} construct, which provides an abstract form of
task parallelism in HPF.
\end{enumerate}
Although they are separate constructs, these features have a strong
interaction.  {\tt RESIDENT} requires a notion of where an operation
is being performed in order to make its assertion; this information is
typically supplied by an {\tt ON} directive.  Similarly, the {\tt
TASKING} feature uses {\tt ON} blocks to identify the parallel tasks.
We therefore discuss {\tt ON} in the first section below, and take up
{\tt RESIDENT} and {\tt TASKING} in Sections~\ref{sec-resident}
and~\ref{sec-tasking}, respectively.



\section{The ON Directive}
\label{sec-on}


The purpose of the {\tt ON} directive is to allow the programmer to
control the  
distribution of computations among the processors of a parallel machine.  
In a sense, this is the dual of the {\tt DISTRIBUTE} and {\tt ALIGN}
directives for  data.
Modern parallel machines will achieve their best performance if all 
operations are performed by separate processors (as specified by {\tt
ON}) with  
each processor accessing its local data (as specified by {\tt DISTRIBUTE}).  
As such, the highest-performing programs will be those for which the
computation partitioning and data mapping work in synergy.
The definition of the {\tt ON} directive is designed to promote this
synergy by referring to the locations of data in order to define the
location of computation.



\subsection{Syntax of the ON Directive}

There are three flavors of the {\tt ON} directive: a single-statement form, a 
multi-statement form, and a declaration form. 
The BNF for these directives is

\BNF
simple-on-directive \IS ON  home-expr [ , resident-clause ] [, new-clause ]

decl-on-directive \IS ENVIRONMENT :: simple-on-directive

block-on-directive \IS simple-on-directive BEGIN

on-block \IS    block-on-directive
        block
        end-directive

end-directive \IS END [ BEGIN ]

home-expr \IS HOME( variable )
        \OR HOME( template-elmt )
        \OR ( processors-elmt )

template-elmt \IS template-name [ ( section-subscript-list ) ]

processors-elmt \IS processors-name [ ( section-subscript-list ) ]
\FNB

\begin{constraints}
\item Any expressions in the {\it home-expr\/}
of a {\it decl-on-directive\/} must be specification expressions.
(Expressions in a {\it simple-on-directive} that is not part of a {\it
decl-on-directive\/} are not so constrained.)
\end{constraints}


{\it resident-clause\/} will be defined in Section~\ref{sec-resident}.
For the present, it suffices to say that this is a form of the {\tt RESIDENT}
directive mentioned in the introduction.

{\it home-expr}, {\it template-elmt}, and {\it processors-elmt\/} 
are just auxiliary syntax 
categories.  
Note that {\it variable\/} is a Fortran syntax term that means 
(roughly) ``a reference, including an array element, array section, or 
derived type field''; {\it variable\/} doesn't include template or processor 
elements since those are not first-class language constructs.  
Note also that {\it block\/} is a Fortran syntax term for 
``a series of statements treated as 
a group'' --- for example, the body of a {\tt DO} construct.

{\it simple-on-directive\/} is an option under {\it
executable-directive\/} (see rule~\ref{executable-directive-rule}).  
This means that 
{\it simple-on-directive\/} can appear where an executable statement can.

{\it decl-on-directive\/} is an option under {\it
specification-directive\/} (see rule~\ref{specification-directive-rule}), as 
{\it distribute-directive\/} is now. 
 This means that {\it decl-on-directive\/} can appear 
where a declaration can.  

{\it on-block\/} most naturally fits as a Fortran {\it
executable-stmt}.
This implies that such blocks are properly nested.


\begin{rationale}
Note the use of parentheses in the last option of the home-expr rule
(involving processors-elmt).
This prevents the following ambiguity:
\CODE
      INTEGER X(4)          ! X(I) will be on processor I
!HPF$ PROCESSORS HOME(4)
!HPF$ DISTRIBUTE X(BLOCK)
      X = (/ 4,3,2,1 /)
!HPF$ ON HOME(X(2))
      X(2) = X(1)
\EDOC
If the parentheses were not required, where should the computation be
done?
\begin{enumerate}
\item Processor HOME(2) (i.e. the owner of X(2))?
\item Processor HOME(3) (i.e. use the value of X(2), before the assignment)?
\item Processor HOME(4) (i.e. use the value of X(2), after the
assignment)?
\end{enumerate}
The definition of {\tt ON} clearly indicates interpretation 1 is correct.  One 
can get the effect of interpretation 2 by the directive
\CODE
!HPF$ ON(HOME(X(2)))
\EDOC
There is no way to get the effect of interpretation 3, short of building a 
clairvoyant computer.  
Introducing reserved keywords into Fortran was 
suggested as a better solution to this problem, but was seen as too large a 
change to the underlying language.

Separate syntax is needed for simple-on-directive and decl-on-directive 
to avoid ambiguity.  If the same directive can be used as both both an 
executable statement and a declaration, its role is unclear if it is the 
last statement in the declarations/first statement in the executable 
section.  This is particularly bad since the "scope" of the directive is 
rather different in the two uses.
\end{rationale}

 
\subsection{Semantics of the ON Directive}

The {\tt ON} directive advises the compiler to perform a computation using the 
processor(s) named in the {\it home-expr}.  It has three forms:
\begin{itemize}
\item {\it simple-on-directive\/} and {\it on-block}, which apply to
the next executable  statement or a block of executable statements,
respectively. 
\item {\it decl-on-directive}, which is a declaration for an entire scope.
\end{itemize}
Like the mapping directives {\tt ALIGN} and {\tt DISTRIBUTE}, this is
advice rather  than an absolute commandment; 
the compiler may override an {\tt ON} directive.  
Also like {\tt ALIGN} and {\tt DISTRIBUTE}, the {\tt ON} directive may
affect the  efficiency of computation, but not the final results.

\begin{implementors}
If the compiler may override the user's advice in an {\tt ON} directive, then 
the compiler should also offer the user an option to force all directives 
to be obeyed.
\end{implementors}

The single-statement {\tt ON} directive (i.e. {\it
simple-on-directive}) precedes the  
statement for which it is advising behavior, and is said to apply to that 
statement.  If the statement is a compound statement (e.g.  a {\tt DO}
loop or an  {\tt IF}-{\tt THEN}-{\tt ELSE} construct), then the {\tt
ON} directive also applies to all nested
statements therein.  
Similarly, the block {\tt ON} directive (i.e.  {\it on-block}) 
applies the initial {\tt ON} clause to all statements up to the
matching {\tt END} directive.  
The declarative form of the {\tt ON} directive (i.e.  
{\it decl-on-directive}) applies to all statements and declarations in
a scope;
its intended use is for functions and subroutines that may be called on a 
subset of the processors.

The {\tt HOME} clause can name a program variable, a template, or a processors 
arrangement.  
For each of these possibilities, it can further specify a 
single element or multiple elements.  
This is translated into the 
processor executing the computation as follows:
\begin{itemize}
\item   If the {\tt HOME} clause names a program variable (that is, an
        array element  
        or section), then every processor owning any part of that variable 
        should execute the computation.  For example, if a is a
        distributed array, then
\CODE
!HPF$ ON HOME ( a(2:4) )
\EDOC
        tells the compiler to perform the statement on the processors owning 
        {\tt a(2)}, {\tt a(3)}, and {\tt a(4)}.  
        If {\tt a} were distributed {\tt BLOCK}, this might be one 
        processor; if it were distributed {\tt CYCLIC}, it would be
        three processors (assuming that many processors were available).
\item   If the {\tt HOME} clause names a template element or section,
        then every processor owning any element of the template should
        execute the computation. 
        The example above applies here as well, if {\tt a} is a
        template rather than an  array.
\item   If the {\tt HOME} clause names a processors arrangement, then
        the processor(s)
        referenced there should execute the computation.  
        For example, if {\tt p} is a processors arrangement, then
\CODE
!HPF$ ON ( p(2:4) )
\EDOC
        will execute the following statement on the three processors
        {\tt p(2)}, {\tt p(3)}, and {\tt p(4)}.
\end{itemize}
For the executable forms of the directive, the values of expressions
in the {\it home-expr\/}
are determined as if the expression was evaluated when control flow 
reached the {\tt ON} directive.  
For the declarative form, the values are determined on entry to the scope.  
That is, if the value of a variable used 
in the {\tt HOME} clause changes within an {\it on-block}, work is not
migrated to a  new processor.  
If evaluation of an expression in a {\tt HOME} clause would 
change the value of any variable in the program, then the value of that 
variable becomes undefined after the {\tt ON} clause is reached.  

In every case, the {\tt ON} directive specifies the processor(s) which should 
perform a computation.  This means that these processors should execute all 
operations required to execute the statements {\em except\/} (perhaps) for the 
initial access of data and writing of results.  
For example, consider the directive and statement
\CODE
        !HPF$ ON HOME( Z(2) )
        X(1) = X(1) + Y(2) * Z(3)
\EDOC
Assume that {\tt X}, {\tt Y}, and {\tt Z} are distributed in some way.
Following the {\tt ON} directive, the statement would be executed as
follows:
\begin{enumerate}
\item   The values of {\tt X(1)}, {\tt Y(2)}, and {\tt Z(3)} are made
        available to the processor owning {\tt Z(2)}.  
        Depending on the hardware running the program, 
        this might correspond to one processor loading registers from
        memory, or 
        it might mean three processors sending messages (and one processor 
        receiving them).
\item   Processor {\tt HOME(Z(2))} performs an addition and a
        multiplication, using the values sent in the last step.  
        That previous data movement allows these operations 
        to be performed locally.
\item   The result is stored to {\tt X(1)}, which may be on a
        different processor  than {\tt Z(2)}.  
        Again, this may require synchronization or other 
        cross-processor operations.
\end{enumerate}
There are considerable subtleties of this scheme when one of the
statements involved is a function or subroutine call.
Section~\ref{sub-on-subr} deals with these cases.
Note that the {\tt HOME} clause only specifies how computation is partitioned 
among processors; it does not indicate processors that may be involved in 
data transfer.  
Also, the {\tt ON} clause by itself does not guarantee that its 
body can be executed in parallel with any other operation.  However, 
placing the computation can have a significant effect on data
locality.
As later examples will show, the combination of {\tt ON} and {\tt
INDEPENDENT} can also  
provide control over load balancing parallel computations.

\begin{rationale}
This is the heart of the {\tt ON} clause.  It defines where computation is 
performed, but not (by itself) what data are accessed.

The ``as if'' wording and making side effects undefined avoids the following 
problem: 
{\tt ON} is a directive.  Therefore, it cannot have side effects.  But 
implementing the {\tt ON} clause may require evaluating some
functions, thereby causing the side effects.
Moreover, different systems may use different implementation
mechanisms.
Such dependences on the implementation mechanism are outlawed by
making their effect undefined.
\end{rationale}

\begin{implementors}
If the HPF program is compiled into Single-Program-Multiple-Data (SPMD) 
code, then the {\tt ON} clause can always be implemented (albeit
inefficiently) 
by having all processors compare their processor id to an id (or list of 
ids) generated from the {\tt HOME} clause.  
(Similar naive implementations can be constructed in other paradigms
as well.)
If the {\tt ON} clause will be executed 
repeatedly, for example in a {\tt DO} loop, it is probably worthwhile
to invert this process.  
That is, instead of all processors executing all the {\tt HOME}
clause tests, the compiler should determine the range of loop iterations 
that will test true on the local processor.  
(See the ``Advice to implementors'' in Section~\ref{sub-on-examples}
for more details.)
For example, consider the following complex case:
\CODE
DO I = 1, N
    !HPF$ ON HOME( A(MY_FCN(I)) ) BEGIN
        ...
    !HPF$ END BEGIN
END DO
\EDOC
Here, the generated code can perform an ``inspector'' (i.e.  a skeleton loop 
that only evaluates the {\tt HOME} clause of each iteration) 
to produce a list of 
iterations assigned to each processor.  
This list can be produced in 
parallel, since {\tt MY\_FCN} must be side-effect free (at least, the
programmer cannot rely on any side effects).
However, distributing the {\it home-expr} computation
to all processors may require unstructured communications patterns, 
possibly negating the advantage of parallelism.  In general, more advanced 
compilers will be able to efficiently invert more complex {\tt HOME}
clauses.
It is recommended that the abilities (and limitations) of a particular 
compiler be documented clearly for users.

Note that processors "screened out" by the naive implementation may still 
be required to participate in data transfer.  
If the underlying architecture 
allows one-sided communication (e.g. shared memory or {\tt GET}/{\tt
PUT}), this is not a problem.  
On message-passing machines, a request-reply protocol may be used.  This 
requires the inactive processors to enter a wait loop until the {\tt ON} block 
completes, or requires the runtime system to handle requests 
asynchronously.  Again, it is recommended that the documentation tell 
programmers which cases are likely to be efficient and which inefficient 
on a particular system.
\end{implementors}

\begin{users}
The form of the {\it home-expr\/} in an {\tt ON} directive can be
arbitrarily complex.  
This is a two-edged sword; 
it can express very complicated computation partitioning, 
but the implementation of these partitions may not be efficient.  More 
concretely, it may express a perfectly load-balanced computation, but force 
the compiler to serialize the computation to implement the {\tt HOME}
clauses.
Although 
the amount of overhead for an {\tt ON} clause will vary based on the HPF code, 
the compiler, and the hardware, one can expect that compilers will generate 
very good code based solely on array mappings or a named processor 
arrangement, and progressively worse code as the complexity of the
{\it home-expr\/} increases.  
A rough measure of the complexity of an {\tt ON} directive is 
the amount of run-time data used to compute it; for example, a constant 
offset is fairly simple, while a permutation array is very complex.  See 
Section~\ref{sub-on-examples} below for more concrete examples of this
phenomenon. 

It is worth noting that the {\tt ON} clause alone does not address
data movement.
(The {\tt RESIDENT} directive defined in Section~\ref{sec-resident}
does this.)
Therefore, on some machines additional 
processors will have to enter the {\tt ON} block to take part in communication.

It should also be noted that the {\tt ON} clause does not change the semantics 
of a program, in the same sense that {\tt DISTRIBUTE} does not change 
semantics.  In particular, an {\tt ON} clause {\em by itself\/} does
not change  sequential code into parallel code, 
because the code in the {\tt ON} block can 
still interact with code outside the {\tt ON} block.  
(To put it another way, {\tt ON} does not spawn processes.)  
\end{users}

It is legal to nest {\tt ON} directives, if the set processors
named by  the inner {\tt ON} directive is included in the set of
processors named by the outer directive.  
The syntax 
of {\it on-block\/} automatically ensures that it is properly nested
inside other 
compound statements, and that compound statements properly nest inside of 
it.  
As with other Fortran compound statements, transfer of control to 
the interior of an {\it on-block\/} from outside the block is
prohibited, while  transfers within a block may occur.  
However, HPF {\em also\/} prohibits transfers 
of control from the interior of an {\it on-block\/} to outside the
{\it on-block}.
Note that this is stricter than in ordinary Fortran.  
If {\tt ON} clauses are nested, then the 
innermost {\it home-expr\/} effectively controls execution of the
statement(s).
A programmer can think of this as successively restricting the set of 
processors at each level of {\tt ON} nesting; 
clearly, the last restriction must be the strongest.  
Alternately, the programmer can think of this as a 
fork-join approach to nested parallelism.

\begin{rationale}
The restrictions about control flow into and out of an {\tt ON} block
essentially  
make it a single-entry single-exit region, thus simplifying the semantics 
considerably.
\end{rationale}


Operations controlled by an {\tt ON} clause must obey certain restrictions:
\begin{itemize}

\item If an {\tt ON} directive applies to a {\tt DISTRIBUTE} directive
whose {\it distributee} is a local variable with neither the
{\tt SAVE} nor the {\tt ALLOCATABLE} attribute, 
then the set of processors named in the {\it home-expr\/} must include
\begin{itemize}
\item All processors named in the {\it DISTRIBUTE}'s {\tt ONTO} clause
if one is present
\item All processors in the default processors arrangement otherwise
\end{itemize}

\item If an {\tt ON} directive applies to a {\tt ALIGN} directive
whose {\it alignee\/} is a local variable with neither the {\tt SAVE}
nor {\tt ALLOCATABLE} attribute, then the set of processors named in
the {\it home-expr\/} must include
all processors that store any element of the {\it align-with-clause}.

\item If an {\tt ON} directive applies to a {\tt REDISTRIBUTE} directive,
then the set of  processors named in the {\it home-expr} must include 
\begin{itemize}
\item All processors that stored any element of the {\it
distributee\/} before the {\tt REDISTRIBUTE} was encountered
\item The processors required by an equivalent {\tt DISTRIBUTE}
directive
\end{itemize}

\item If an {\tt ON} directive applies to a {\tt REALIGN} directive,
then the set of processors named in the {\it home-expr\/} must include
\begin{itemize}
\item All processors that stored any element of the {\it alignee} before 
          the {\tt REALIGN} was encountered
\item The processors required by an equivalent {\tt ALIGN} directive
\end{itemize}

\item If an {\tt ON} directive applies to an {\tt ALLOCATE} statement
which creates an explicitly mapped variable, then the set of
processors named in the {\it home-expr\/} 
must include the processors required by the mapping directive for the 
allocated variable.  

\item If the {\tt ON} directive applies to a 
{\tt DEALLOCATE} statement that destroys an explicitly mapped
variable, then the {\it home-expr\/} must include all processors that
owned any element of that variable.
\end{itemize}
If operations within an {\tt ON} block do not follow these
rules, then the  program is not HPF-conforming.

{\bf Note to language designers:}\\
An alternative for the DISTRIBUTE would be that an missing {\tt ON}TO clause 
would mean "distribute on all processors in the nearest enclosing {\tt ON} 
directive" rather than "distribute on all processors".  In some sense, this 
makes the nested fork-joins more modular (declarations inside a forked 
region only need to know about the region they are part of).  It is 
especially appropriate now that we have the declarative {\tt ON} directive.  I 
have not investigated the difficulty of writing things this way, but it 
probably requires fine-tooth combing through the data mapping chapter and 
inquiry intrinsics.\\
{\bf End of note to language designers.}

\begin{rationale}
Operations which allocate memory require the cooperation of all processors 
that will own that memory.  Therefore, {\tt ON} clauses must schedule those 
operations to execute on the cooperating processors.  This leads to 
constraints on the mappings of variables allowed in {\tt ON} clauses.
The most 
common case where these apply is in subroutines called from {\tt ON} clauses; 
such subroutines must have a declarative {\tt ON} clause that applies to all 
{\tt DISTRIBUTE} and {\tt ALIGN} directives for local variables, dummy
arguments, and  global data.

An alternate description of these constraints is:
\begin{itemize}
\item Local variables that are not {\tt SAVE}d can only be mapped to
  the processors 
  executing the surrounding {\tt ON} clause.  This ensures that all local 
  variables are allocated within the {\tt ON} processor set, and that
  all references to local variables will be {\tt RESIDENT} as defined below.
\item Dummy arguments and result variables can only be mapped to the
  processors 
  executing the {\tt ON} clause.  Like local variables, this ensures that all 
  references to dummies and result variables are to local memory.  Note 
  that, although the dummy arguments must be {\tt RESIDENT}, the
  actual argument may not be (due to remapping).
\item Global variables may be explicitly mapped onto all processors
  (or onto any 
  subset of processors that could normally be used).  This is required so 
  that the mappings of the globals can be consistent in different scopes.  
  Memory for the global variables will be allocated either at load time, 
  when all processors are active, or in explicit {\tt ALLOCATE} statements, 
  which will be dealt with below.
\item Local variables with the {\tt SAVE} attribute can be mapped onto
  any set of  
  processors.  In this sense, they are much like global variables.  Like 
  global variables, it is possible to ensure that an appropriate set of 
  processors is active when memory is allocated for them.
\item {\tt ALLOCATABLE} variables have their mapping determined when they are 
  allocated.  Therefore, the restrictions on those mappings are applied to 
  the {\tt ALLOCATE} statement.
\end{itemize}
\end{rationale}

\begin{implementors}
These restrictions ensure that HPF data distribution directives inside 
an {\tt ON} block (either lexically or in a dynamic call chain) can be 
implemented without relying on one-way communication outside of the 
``current'' processing group.
\end{implementors}

If an {\tt ON} directive includes a {\tt NEW} clause, the meaning is
the same as a {\tt NEW}
clause in an {\tt INDEPENDENT} directive.  
The operation of the program would be 
identical if the {\tt NEW} variables were allocated anew on every entry to the 
{\tt ON} directive's scope, and deallocated on exit from the {\tt ON}
block.
That is, the {\tt NEW} variables are dead on entry (i.e. assigned
before use in the 
{\tt ON} block) and dead on exit (i.e. not used after the {\tt ON}
block, unless first  reassigned).  
In addition, {\tt NEW} variables cannot be remapped in the {\tt ON} 
clause's scope, whether by {\tt REALIGN}, {\tt REDISTRIBUTE}, or by
parameter passing to subroutine calls.  
Finally, {\tt NEW} variables are not considered by any nested {\tt RESIDENT}
directives, as detailed in Section~\ref{sec-resident}.

\begin{rationale}
{\tt NEW} clauses provide a simple way to create temporary variables.  This 
ability is particularly important when {\tt RESIDENT} directives come
into play, as  will be clear below.
\end{rationale}

\begin{implementors}
Because they are not used outside of the {\tt ON} blocks, {\tt NEW}
variables need not be kept consistent before and after {\tt ON}
clauses.  
Therefore, no communication outside of the {\tt ON} processor set is
required to implement  them.  
Scalar {\tt NEW} variables should be replicated over the {\tt ON}
processor set,  
or allocated to memory areas shared by the {\tt ON} processor set.  
Note that memory must be dynamically allocated if there is a possibility that 
multiple instances of the {\tt ON} block could be active concurrently.
This is similar to the requirements for implementing {\tt NEW}
variables in {\tt INDEPENDENT} loops.
\end{implementors}


\subsection{ON Directives Applied to Subprogram Invocations}
\label{sub-on-subr}


It is legal for an {\tt ON} directive to apply to a {\tt CALL}
statement or a statement  containing a function invocation.  
The {\tt ON} directive tells the compiler 
which processors should execute the statements in the procedure body.
Any procedure which is called from a statement controlled by an {\tt
ON} directive must have an explicit interface in the caller.  
Furthermore, the interface must include a valid declarative {\tt ON}
directive which applies to the entire called procedure.  
(I.e.  If an {\tt INTERFACE} block is used, 
then the {\tt INTERFACE} specification must include an
{\tt ENVIRONMENT ::  ON} clause.)  
The treatment of {\tt ON} clauses in the interface is similar to that 
for a compound statement.  Any processor named by an {\tt ON} directive inside 
the subroutine must be included by the {\tt ON} directive in the caller.  In 
particular, the declarative {\tt ON} directive in the interface must name a 
subset of the processors in the caller's {\tt ON} clause, and any {\tt
ON} clauses in  
the subroutine itself can only restrict the declarative {\tt ON} directive's 
processor set further.  If {\tt ON} clauses appear in a subroutine call chain, 
then the deepest {\tt ON} clause (i.e.  the one in the last called
routine that is still active) effectively controls the computation.

Note that {\tt EXTRINSIC} procedures always have an explicit
interface, and thus  will require an {\tt ON} declaration if they are
called from an {\tt ON} block.  
In this case, the effect of the call is still as if the procedure were called 
on all processors.
 
If the procedure uses alternate return, then the target of the return must 
be in the same {\tt ON} block as the CALL statement.  This implies that labels 
passed as arguments must refer to statements in the same {\tt ON} block as the 
{\tt CALL} statement.

\begin{rationale}
It is natural to treat a procedure call within an {\tt ON} clause as
if it were  an in-lined program block.  
This leads to "propagating" the {\tt ON} directive 
into the procedure.  
Making the {\tt ON} directive explicit in the callee allows 
separate compilation (i.e.  the compiler need not perform interprocedural 
analysis in order to select the calling convention).

The constraint on alternate return is similar to the prohibition against 
jumping out of an {\tt ON} block, and has the same justification.
\end{rationale}

\begin{implementors}
Notice that nested {\tt ON} clauses do not present additional problems for the 
naive implementation.  If a processor failed the outer {\it home-expr}
comparison,  then it would fail any tests inside the {\tt ON} as well.
Thus, it need not even make the tests.

The difficulties of implementing one-way communication on message-passing 
machines remain, however.
\end{implementors}

\begin{users}
A {\tt CALL} statement from within an {\tt ON} block effectively executes the 
subroutine on a subset of processors.  In conjunction with other 
declarations, this allows a fork-join style of parallelism.

Note that the earlier advice regarding data movement still applies.  
Message-passing machines may need to perform the call statement on many 
(even all) processors in order to properly exchange data between 
processors.
\end{users}



Explicit use of processors arrangements in {\tt ON} directives is usually 
associated with task parallelism.  Several examples can be found
there.
The following example illustrates how processors can be used 
for a one-dimensional domain decomposition algorithm:
\CODE
        !HPF$ PROCESSORS PROCS(NP)
        !HPF$ DISTRIBUTE X(BLOCK) ONTO PROCS

        ! Compute ILO(IP) = lower bound on PROCS(IP)
        ! Compute IHI(IP) = upper bound on PROCS(IP)
        DONE = .FALSE.
        DO WHILE (.NOT. DONE)
          !HPF$ INDEPENDENT
          DO IP = 1, NP
            !HPF$ ON (PROCS(IP))
            CALL SOLVE_SUBDOMAIN( IP, X(ILO(IP):IHI(IP)) )
          END DO
          !HPF$ ON HOME(X) BEGIN
            CALL SOLVE_BOUNDARIES( X, ILO(1:NP), IHI(1:NP) )
            DONE = CONVERGENCE_TEST( X, ILO(1:NP), IHI(1:NP) )
          !HPF$ END BEGIN
        END DO
\EDOC
The algorithm divides the entire computational domain (array {\tt X})
into {\tt NP} 
subdomains, one for each processor.  The {\tt INDEPENDENT} {\tt IP}
loop performs a computation on each subdomain's interior.  
The {\tt ON} directive tells the compiler which processors to use in
executing these (conceptually) parallel operations. This can increase
data locality substantially, particularly if the computiler could not
otherwise analyze the data access patterns in {\tt SOLVE\_SUBDOMAIN}.
The subroutine {\tt SOLVE\_SUBDOMAIN} can use a transcriptive or descriptive
mapping for its array argument, placing it on a single processor.  
In the next phase, the processors collaborate 
to update the boundaries of the subdomains and test for convergence.  
Subroutines {\tt SOLVE\_BOUNDARIES} and {\tt CONVERGENCE\_TEST} may
well have their own loops similar to the {\tt IP} loop, with 
similar {\tt RESIDENT} clauses.  
Note that only the lower and upper bounds of each 
subdomain is recorded; this allows different processors to process 
different-sized subdomains.  However, each subdomain must ``fit'' into one 
processor's section of the {\tt X} array.

\begin{implementors}
The {\tt IP} loop above is likely to be a common idiom among programmers doing 
block-structured codes.  In general, it can be implemented by inverting the 
{\tt HOME} clause as was done above.  
In the one-to-one case shown here (probably 
very popular with programmers), it can be implemented by assigning the 
processor id to the loop index variable and testing the range of the loop 
(once).
\end{implementors}

\begin{rationale}
Some compilers will propogate the {\tt ON} information from the caller to the 
callee at compile time, and some at run time.  
Repeating the {\tt ON} clause in 
the caller and callee will tend to give the compiler better information, 
resulting in better generated code.  
\end{rationale}


\subsection{Examples of ON Directives}
\label{sub-on-exapmles}

The following are valid examples of {\tt ON} directives.  Most of them are 
``reasonable'' in the sense that they illustrate idioms that programmers 
might want to use, rather than contrived situations.  For simplicity, the 
first several examples assume the following array declarations:
\CODE
        REAL A(N), B(N), C(N), D(N)
        !HPF$ DISTRIBUTE A(BLOCK), B(BLOCK), C(BLOCK), D(BLOCK)
\EDOC
One of the most commonly requested capabilities for HPF as to control how 
loop iterations were assigned to processors.  
(Historically, the {\tt ON} clause 
first appeared to perform exactly this role in the Kali FORALL construct.) 
This can be done by the {\tt ON} directive, as shown in the following examples:
\CODE
        !HPF$ INDEPENDENT
        DO I = 2, N-1
          !HPF$ ON HOME(A(I))
          A(I) = (B(I) + B(I-1) + B(I+1))/3
        END DO
        
        !HPF$ INDEPENDENT
        DO J = 2, N-1
          !HPF$ ON HOME(A(J+1)) BEGIN
            A(J) = B(J+1) + C(J+1) + D(J+1)
          !HPF$ END BEGIN
        END DO
\EDOC
The {\tt ON} directive in the {\tt I} loop advises the compiler to
have each processor  
run over its local section of the {\tt A} array (and therefore {\tt B}
as well).  
The references to {\tt B(I-1)} and {\tt B(I+1)} must be fetched from
off-processor for the  
first and last iterations on each processor (except for the boundary 
processors); note that those processors are not mentioned in the {\tt HOME} 
clause.  The {\tt ON} directive in the {\tt J} loop advises the
compiler to ``shift''  
computations so that each processor does a vector sum of its local sections 
of {\tt B}, {\tt C}, and {\tt  D}, stores the first element of the
result on the processor to  
its left, and stores the rest of the result (shifted by one) in {\tt A}.
It is worth noting that the directives would still be valid (and minimize 
nonlocal data accesses) if the arrays were distributed {\tt CYCLIC},
although the number of nonlocal references would be much higher.

\begin{implementors}
It is highly recommended that compilers concentrate on optimizing DO loops 
with a single {\tt ON} clause including the entire loop body.  Schematically, 
the code will be:
\ICODE
        DO i = lb, ub, stride
            !HPF$ ON HOME(array(f(i))) BEGIN
            body
            !HPF$ END BEGIN
        END DO
\EDOC
Where array has some data mapping.  Assume the mapping give processor p 
the elements my_set(p).  (In a BLOCK distribution, for example, my_set(p) 
is a contiguous range of integers.)  Then the generated code on processor 
p should be
\ICODE
        DO i in [lb:ub:stride] intersect finverse(my_set(p))
                body
        END DO
\EDOC
(This schematic does not show where communication or synchronization must 
be placed; that must be derived from analysis of the body.) Moreover, $f$ is 
likely to be the identity function or a linear function with integer 
coefficients, both of which can be inverted easily.  Given this, techniques 
for iterating through the set can be found in several recent conferences.
\end{implementors}

\begin{users}
One can expect the {\tt I} loop above to generate efficient code for the 
computation partitioning.  In effect, the compiler will arrange for each 
processor to iterate over its own section of array {\tt A}.  The {\tt
J} loop is  slightly more complex, since the compiler must find the
inverse of the {\tt HOME} 
clause's subscripting function.  That is, the compiler must solve 
{\tt K=J+1} for {\tt J}, where {\tt K} ranges over the local elements
of {\tt A}.  
Of course, in this case {\tt J=K-1}; in general, linear functions can
be inverted by the compiler.  
(It should be pointed out, however, that complex combinations of {\tt
ALIGN} and  {\tt DISTRIBUTE} may make the description of {\tt K}
unwieldy, and this may add overhead to the inversion process.) 
\end{users}
 

Sometimes it is advantageous to "split" an iteration between processors. 
The following case shows one example of this:
\CODE   
        !HPF$ INDEPENDENT
        DO I = 2, N-1
          !HPF$ ON HOME(A(I))
          A(I) = (B(I) + B(I-1) + B(I+1))/3
          !HPF$ ON HOME C(I+1)
          C(I+1) = A(I) * D(I+1)
        END DO
\EDOC
Due to the first {\tt ON} clause, the reference to {\tt A(I)} is local
in the first statement. 
The second {\tt ON} clause makes {\tt A(I)} nonlocal (for some values
of {\tt I}) 
there.  This maximizes the data locality in both statements, but does 
require data movement between the two.  

\begin{implementors}
If there are several non-nested {\tt ON} clauses in a loop, then the schematic 
above needs to be generalized.  In essence, the iteration range for each 
individual {\tt ON} clause must be generated.  
A processor will then iterate over the union of these ranges. 
Statements guarded by an {\tt ON} directive must now 
be guarded by an explicit test.  In summary, the code for
\ICODE
        DO i = lb, ub, stride
                !HPF$ ON HOME(array_1(f_1(i)))
                stmt_1
                !HPF$ ON HOME(array_2(f_2(i)))
                stmt_2
        END DO
\EDOC
on processor $p$ becomes 
\ICODE
        set_1 = [lb:ub:stride] intersect f_1inverse(myset_1(p))
        set_2 = [lb:ub:stride] intersect f_2inverse(myset_2(p))
        DO i in set_1 union set_2
          IF (i in set_1) THEN
            stmt1
          END IF
          IF (i in set_2) THEN
            stmt2
          END IF          
        END DO
\EDOC
where $myset_1(p)$ is the local set for $array_1$, and $myset_2(p)$ is
the local set for $array_2$.  
(Again, synchronization and communication must be handled 
by other means.)  Code transformations such as loop distribution and loop 
peeling can be used to eliminate the tests in many cases.  They will be 
particularly profitable if there are data dependences between the {\tt ON} 
blocks.
\end{implementors}

\begin{users}
Splitting an iteration like this is likely to require either additional 
tests at runtime or additional analysis by the compiler.  Even if the 
compiler can generate low-overhead scheduling for the individual {\tt ON} 
clauses, combining them is not necessarily low-overhead.  The locality 
benefits must be rather substantial for this to pay off, but there are 
cases where multiple {\tt ON} clauses are valuable.  (All these statements are 
particularly true if one {\tt ON} block uses data computed in another one.)
\end{users}


Because {\tt ON} clauses nest naturally, they can be useful for expressing 
parallelism along different dimensions.  Consider the following examples:
\CODE
        REAL X(M,M)
        !HPF$ DISTRIBUTE X(BLOCK,BLOCK)
        
        !HPF$ INDEPENDENT, NEW(I)
        DO J = 1, M
          !HPF$ ON HOME(X(:,J)) BEGIN
            DO I = 2, M
              !HPF$ ON HOME(X(I,J))
              X(I,J) = (X(I-1,J) + X(I,J)) / 2
            END DO
          !HPF$ END BEGIN
        END DO
\EDOC
Each iteration of the {\tt J} loop is executed by a column of the processors 
arrangement.  The {\tt I} loop further subdivides the computation, giving each 
processor responsibility for computing the elements it owns.  Many 
compilers would have chosen this computation partitioning automatically for 
such a simple example.  However, the compiler might have attempted to fully 
parallelize the outer loop, executing each inner loop sequentially on one 
processor.  (This might be attractive on a machine with very fast 
communications.) 
By inserting the {\tt ON} clauses, the user has advised against 
this strategy, thus trading additional locality for restricted parallelism.  
Notice that the {\tt ON} directive neither requires nor implies the
{\tt INDEPENDENT} assertion.  
In both nests, each iteration of the {\tt I} loop depends on the 
preceeding iteration, but the {\tt ON} directive can still partition the 
computation among processors.  
The {\tt ON} directive does not automatically make a loop parallel.

\begin{implementors}
``Dimension-based'' nesting, as above, will probably be a common case.  The 
{\tt HOME} clauses can be inverted at each level, treating indices from outer 
loops as run-time invariants.
\end{implementors}

\begin{users}
Nested {\tt ON} directives will tend to have efficient implementations
if their {\tt HOME} clauses refer to different dimensions of the
processors arrangements, as in the above example.  
This minimizes the interaction between the levels 
of the loops, simplifying the implementation.
\end{users}

Consider the following variation on the above example:
\CODE
        !HPF$ DISTRIBUTE Y(BLOCK,*)

        !HPF$ INDEPENDENT, NEW(I)
        DO J = 1, M
          !HPF$ ON HOME(Y(:,J)) BEGIN
            DO I = 2, M
              !HPF$ ON HOME(Y(I,J))
              Y(I,J) = (Y(I-1,J) + Y(I,J)) / 2
            END DO
          !HPF$ END ON
        END DO
\EDOC
Note that the {\tt ON} clauses have not changed, except for the name of the 
array.  The interpretation is similar to the above, except that the outer 
{\tt ON} directive assigns each iteration of the {\tt J} loop to all
of the processors.  
The inner {\tt ON} directive again implements a simple owner-computes
rule.  
The programmer has directed the compiler to distribute a serial computation 
across all the processors.  There are a few scenarios where this is more 
efficient than parallelizing the outer loop:
\begin{enumerate}
\item Parallelizing the outer loop will generate many non-local references, 
   since only a part of each column is on any processor. 
   If non-local references 
   are very expensive (or if {\tt M} is relatively small), this overhead 
   may outweigh any gain from parallel execution.
\item The compiler may take advantage of the {\tt INDEPENDENT}
   directive to avoid inserting any synchronization.  
   This allows a natural pipelined execution.  
   A processor will execute its part of the {\tt I} loop for one value
   of {\tt J}, then immediately go on to the next {\tt J} iteration.  
   Thus, the first processor 
   will start on {\tt J=2} while the second receives the data it needs (from 
   processor one) for {\tt J=1}.  (A similar pipeline would develop in
   the {\tt X}  example above.)
\end{enumerate}
Clearly, the suitability of these {\tt ON} clauses will depend on the
underlying parallel architecture.

\begin{users}
This example points out how {\tt ON} may improve software engineering.
While the ``value'' of {\tt HOME(X(I))} will change if {\tt X}'s
mapping changes, its intent will usually stay the same - run the loop
``aligned with'' the array {\tt X}.  Moreover, 
the form of the clauses is portable, and they simplify experimenting with 
alternative computation partitioning.  Both qualities are similar to the 
advantages of {\tt DISTRIBUTE} and {\tt ALIGN} over low-level data
layout mechanisms. 
\end{users}

{\tt ON} directives are particularly useful when the compiler cannot
accurately estimate data locality, for example when the computation
uses indirection arrays.  
Consider three variations of the same loop:
\CODE
        REAL X(N), Y(N)
        INTEGER IX1(M), IX2(M)
        !HPF$ DISTRIBUTE X(BLOCK), Y(BLOCK)
        !HPF$ DISTRIBUTE IX(BLOCK), IY(BLOCK)
        
        !HPF$ INDEPENDENT
        DO I = 1, N
          !HPF$ ON HOME( X(I) )
          X(I) = Y(IX(I)) - Y(IY(I))
        END DO
        
        !HPF$ INDEPENDENT
        DO J = 1, N
          !HPF$ ON HOME( IX(J) )
          X(J) = Y(IX(J)) - Y(IY(J))
        END DO

        !HPF$ INDEPENDENT
        DO K = 1, N
          !HPF$ ON HOME( X(IX(K)) )
          X(K) = Y(IX(K)) - Y(IY(K))
        END DO
\EDOC
In the {\tt I} loop, each processor runs over its section of the {\tt
X} array.  
Only the reference {\tt X(I)} is guaranteed to be local.  
(If \(M \neq N\), then {\tt IX} and {\tt IY} 
have a different block size than {\tt X}, and thus a different mapping.)  
However, if it is {\em usually\/} the case that {\tt X(I)}, {\tt
Y(IX(I))}, and {\tt Y(IY(I))} are 
located on the same processor, then this mapping may be the best one 
available.  If {\tt X(I)} and {\tt Y(IX(I))} are {\em always} on the
same processor, then the {\tt RESIDENT} clause should be added as
explained in Section~\ref{sec-resident}
\CODE
        !HPF$ ON HOME( X(I) ), RESIDENT( Y(IX(I)) )
\EDOC
This will avoid communication setup overhead on most systems, and there is 
little chance that the compiler would deduce this automatically.  If both 
references to {\tt Y} are {\em always} on the same processor as {\tt
X(I)}, then further improvement is possible and desirable, as
explained in Section~\ref{sec-resident}
In the {\tt J} loop, references {\tt IX(J)} and {\tt IY(J)} are always
local.  
This is the most common array reference class in the loop, so it minimizes the 
number of nonlocal data references in the absence of any special 
properties of {\tt IX} and {\tt IY}.  
It may not evenly balance the load among 
processors; for example, if {\tt N=M/2} then half the processors will be idle.
As before, if the values in {\tt IX} or {\tt IY} ensure that one of
the {\tt Y} references is always local, a {\tt RESIDENT} assertion
should be added.  
In the {\tt K} loop, only reference {\tt Y(IX(K))} is guaranteed to be
local (because {\tt Y} and {\tt X} have the same 
distribution).  
However, the values stored in {\tt IX} and {\tt IY} may ensure that 
{\tt Y(IY(K))} and {\tt X(K)} always local.
Even if the three {\tt REAL} values are not always, but merely
``usually'' on the same processor, this may be a good computation
partitioning for both locality and parallelism.  
However, these advantages must be weighed 
against the cost of computing this partitioning.  
Since the {\tt HOME} clause depends on a (presumably large) array of
runtime values, substantial time 
may be required to determine which iterations are assigned to each 
processor.  It should be clear from this discussion that there is no magic 
solution for handling complex computation partitionings; the best answer 
is usually a combination of application knowledge, careful data structure 
design (including ordering of the elements), and efficient compilation 
methodology and runtime support.

\begin{implementors}
The {\tt K} loop is the situation that the inspector strategy
described above is designed for.  
If there is an outer loop around any of these examples, and 
that loop does not modify the distribution of {\tt X} or the values of
{\tt IX}, then a record of each processor's iterations can be saved
for reuse.  
The cost is at worst linear in the sizes of the arrays.
\end{implementors}

\begin{users}
It is unlikely that any current production compiler will generate
low-overhead code for {\tt K} loop.  
The difference from previous examples 
is that the {\tt HOME} clause is not a function that can be easily inverted by 
the compiler.  Some compilers may choose to execute every iteration on all 
processors, testing the {\tt HOME} clause at run-time; others may
pre-compute a 
list of iterations for every processor.  Of course, the cost of computing 
the list will be substantial.

In practice, one would make all the arrays the same size to avoid some of 
the alignment problems above; the example was written this way for 
pedagogical reasons, not as an example of good data structure design.
\end{users}


\section{The RESIDENT Directive}
\label{sec-resident}

The purpose of the {\tt RESIDENT} clause is to work together with the ON
directive to  identify data accessed by 
the computation as local to the executing processor.  
The compiler can use 
this information to avoid generating communication or to simplify
array address  calculations.  
Note that whether a given data element is local depends on 
two facts:
\begin{itemize}
\item   Where the data is stored (i.e. {\tt DISTRIBUTE} and {\tt
ALIGN} attributes for the variable)
\item   Where the computation is executed (i.e. its {\tt ON}
directive)
\end{itemize}
For these reasons, the {\tt RESIDENT} clause is added to the {\tt ON}
directive, which is usually the earliest point in the program
where the needed facts might  be available.  
The {\tt RESIDENT} clause can also appear as a stand-alone directive;
this is useful when the locality information is not true for an entire
{\tt ON} region.
Note that changing the {\tt ON} directive may invalidate some 
{\tt RESIDENT} clauses, or may make some new {\tt RESIDENT} clauses true.
\BNF
resident-clause \IS     RESIDENT [ ( local-var-list ] ) ]

simple-resident-directive \IS resident-clause

block-resident-directive \IS resident-clause BEGIN

resident-block \IS
                block-resident-directive
                block
                end-directive

local-var \IS variable
\FNB
As for {\it simple-on-directive\/}, {\it simple-resident-directive}
will be an option under  {\em executable-directive}
Similarly, {\it resident-block\/} fits as an Fortran {\it executable-stmt}.

Any top-level variables in the {\tt RESIDENT} clause must be explicitly 
mapped.  Otherwise, the assertion (see below) is a statement about how the 
compiler works, not about the program.

{\it On-block} fits most naturally as a Fortran {\it executable-stmt},
since that makes  constraints about ``properly nesting'' easier to state.  

\begin{implementors}
{\tt RESIDENT} removes need for masked processors to
participate in communication into/out of and ON clause.
\end{implementors}


The {\tt RESIDENT} directive is an assertion to the compiler that
certain array references made within the {\tt ON} are stored in local
memory if the computation is performed by the processor(s) named in
nearest enclosing {\tt ON} directive. 
The scope of the assertion is the next Fortran statement if the 
{\it simple-resident-directive\/} form is used and the enclosed {\it
block} of code if the {\it resident-block\/} form is used.  
If {\tt  RESIDENT} appears as a clause in an {\tt ON} 
directive, then the {\tt ON} and {\tt RESIDENT} apply to the same
statements.
In this case, the {\tt RESIDENT} assertion refers to the {\tt ON}
directive in which it  appears.

{\tt RESIDENT(}{\it var}{\tt )} means the {\em lexical expression}
{\it var}, when encountered in the 
execution of statements in the scope of the {\tt RESIDENT} directive, accesses 
only data local to the set of executing processors.  
(That is, the set of processors named by the {\tt ON} directive,
henceforth referred to as the {\tt ON} processors set.)  
If {\it var\/} is accessed by the statement (e.g.  it appears on 
the right-hand side of an assignment statement, or in the evaluation of a 
conditional expression), then at least one copy of the variable and any 
subobject of the variable must be mapped to the {\tt ON} processors
set.  
If {\it var\/} is assigned to by the statement (e.g.  it appears on
the left hand side of an assignment statement, or in the variable list
of a {\tt READ} statement), then 
all copies of the variable and all subobjects of the variable must reside 
in the {\tt ON} processors set.  

Note that {\tt RESIDENT} is always an assertion relative to the
surrounding {\tt ON} directive.  
Therefore, if the compiler does not implement the {\tt ON} directive 
then it must be careful in interpreting {\tt RESIDENT}. 
Similarly, if the compiler overrules the programmer-specified {\tt
ALIGN} and {\tt DISTRIBUTE} directives, the {\tt RESIDENT} clause may
give less information. 

Finally, {\tt NEW} variables are not considered by any nested {\tt RESIDENT}
directives, as detailed below.

\begin{rationale}
The different treatment of variable reads and writes is due to the 
implementation requirements. If a variable's value is read (but not 
written), then it can be taken from any consistent copy.  Therefore, 
{\tt RESIDENT} only asserts that one of those copies is available.  
Conversely, all copies of a replicated variable must be consistent, so
{\tt RESIDENT} asserts that all copies are available it it is updated.

The {\tt RESIDENT} assertion is always relative to the declared data
mappings and  {\tt ON} clauses because both pieces of information are
necessary to determine  the locality of data references.  
Data mapping determines where the data is 
stored, while {\tt ON} clauses determines where they are used; in essence they 
determine the endpoints of a data path.  
{\tt RESIDENT} itself says that the path 
length is very short; obviously, one cannot measure a path without knowing 
both endpoints.
\end{rationale}

For example, consider the following:
\CODE
        !HPF$ ON HOME(Z(I)), RESIDENT(X,Y,RECORD(I))
        X(I) = Y(I+1) + RECORD(I)%FIELD1 + RECORD(I+1)%FIELD2
\EDOC
The following facts are asserted by the directive:
\begin{itemize}
\item {\tt Z(I)} would be local if it appeared, due to its use in the
HOME directive.
\item All copies of {\tt X(I)} are stored on the same processor as
{\tt Z(I)}, due to the {\tt RESIDENT} clause.  This may be true
because {\tt X} and {\tt Z} have the same mapping, or because {\tt Z}
is replicated on all processors, or because the single copy of {\tt
X(I)} is the only element of {\tt X} mapped to the same processor as
the single copy of {\tt Z(I)}.  (Other situations are also possible.)
\item At least one copy of {\tt Y(I+1)} is on the same processor as
{\tt Z(I)}, due to the {\tt RESIDENT} clause.  This may be true
because {\tt Y} is replicated on all processors, because {\tt Z(I)}
and {\tt Y(I+1)} are the only elements of their arrays that are mapped
to the same processor, or because the directive 
\CODE
        !HPF$ ALIGN Y(J) WITH Z(J-1)
\EDOC
appears elsewhere in the program.  (Other situations also make the
{\tt RESIDENT} assertion true.)
\item At least one copy of all subobjects of {\tt RECORD(I)} is mapped
on the same processor as {\tt Z(I)}.  In particular, the reference
{\tt RECORD(I)\%FIELD1} (i.e. a subobject consisting of one component)
can be accessed locally.   The situations in which this is true are
similar to those for {\tt X(I)}.  No information is available in this
example regarding {\tt RECORD(I+1)\%FIELD2}.
\end{itemize}

If there is no {\it local-var-list}, then {\em all\/} references to
{\em all} variables referenced during execution of the {\tt RESIDENT}
directive's body except those declared {\tt NEW} in a surrounding {\tt
ON} directive are local in the sense described above.  
That is, for every usage of any variable's value, at least one copy 
of the variable will be mapped to the {\tt ON} processor set.  Likewise, for 
every operation that assigns to a variable, all copies of that variable are 
mapped to the {\tt ON} processor set.  References and assignments to
{\tt NEW} variables are always considered local.  
If there are no function or 
subroutine invocations, this is syntactic sugar for listing all variable 
references within the directive's scope.  
(See Section~\ref{sub-res-subr} for a discussion of {tt RESIDENT}
caluses applied to subprogram calls.)
It might well have been named the 
{\tt ALL\_RESIDENT} clause; the present form, however, does not add
yet another keyword to the directive sublanguage.

Note that if the {\tt HOME} clause specifies more than one processor,
then {\tt RESIDENT} only asserts that the variables are stored on one
of the processors.  
For example, if a statement is executed on a section of the processors 
arrangement, then communication within that section may be needed for some 
variables in the {\tt RESIDENT} clause.  
Communication with processors outside of 
the section will not be needed for those variables, however.

\begin{rationale}
The alternative to this interpretation would be that any variable named in 
the {\tt RESIDENT} clause would be local to all processors, i.e. replicated.   
While that certainly allows more extensive optimizations, it is a less 
common case.  In addition, it does not seem to capture the intent of {\tt ON} 
directives applied to {\tt CALL} statements or compound statements.  For
example,
\CODE
        !HPF$ PROCESSORS PROCS(MP,MP)
        !HPF$ DISTRIBUTE X(BLOCK,BLOCK) {\tt ON}TO PROCS
        !HPF$ ON HOME(PROCS(1,1:MP)), RESIDENT( X(K,1:N) )
        CALL FOO( X(K,1:N) )
\EDOC
would presumably call {\tt FOO} on a row of the processors
arrangement, passing elements of {\tt X} in place.  
This is what the current definition does; if 
{\tt RESIDENT} meant ``resident on every processor'', the call would
force {\tt X} to be replicated.
\end{rationale}

The {\tt RESIDENT} directive is similar to the {\tt INDEPENDENT}
directive, in that if it is correct it does not change the meaning of
the program.  
If the {\tt RESIDENT} clause is incorrect, the program is not
standard-conforming (and is thus undefined).  
Like the {\tt INDEPENDENT} directive, the compiler may use the 
information in the {\tt RESIDENT} clause, or ignore it if it is
insufficient for the compiler's purposes.  
If the compiler can detect that the {\tt RESIDENT} clause is 
incorrect (i.e.  that a {\tt RESIDENT} variable is definitely nonlocal), it is 
justified in producing a warning.  Unlike the {\tt INDEPENDENT} directive, 
however, the truth of the {\tt RESIDENT} clause depends on the mapping of 
computations (specified with the {\tt ON} clause) and the mapping of data 
(specified with {\tt DISTRIBUTE} and {\tt ALIGN} clauses); if the
compiler overrides either of these, then it may not be able to use
information in the {\tt RESIDENT} directive.

\begin{rationale}
Knowing that a reference is local is valuable information for the 
optimizer.  It is in keeping with the spirit of HPF to phrase this as an 
assertion of fact, which the compiler can use as it pleases.  Expressing 
it as advice to the compiler seems to have disadvantages.  Some possible ways 
this advice could be phrased, and the counter-arguments, are 
\begin{itemize}
\item   ``Don't generate communication for this reference'' has great potential
        for changing the meaning of the program.  Some programmers want this 
        capability, but it violates the ``correct directives should
        not change the meaning of a program'' principle of HPF.  
        Also, once communication is ``turned off'' for a reference,
        it's not clear how to turn it back on.
\item   ``Generate communication for this reference'' is not a useful
        directive,  since the compiler has to do this anyway.
\item   ``Generate communication for this reference, and place it
        here'' is useful, since it can override the default placement by the
        compiler.  
        It still has potential for changing program meaning.  
        It also has the potential to create programs as complex as
        message-passing, as programmers try to move communication out of
        loops. 
\end{itemize}
\end{rationale}


\subsection{RESIDENT Directives Applied to Subprogram Invocations}
\label{sub-res-subr}

If a {\tt RESIDENT} directive applies to a {\tt CALL} statement or
function invocation, then the assertion is more subtle.

\begin{itemize}

\item    If a {\it local-var-list\/} appears in the {\tt RESIDENT}
directive, then no assertion is made about behavior within the called
procedure.  
For example, consider the statements:
\CODE
        !HPF$ RESIDENT( A(I), B )
        A(I) = F( A(I), B(LO:HI) )
\EDOC
The directive declares all variable refences in the statement (including 
the actual parameters) to be local to the current {\tt ON} processor set.  
However, the execution of {\tt F} itself could access elements of arrays named 
{\tt A} and {\tt B} stored on arbitrary processors. 

\begin{rationale}
Propagating assertions about the behavior of lexical entities is difficult 
to define consistently and usefully.  For example, consider the following 
function called from the code fragment above:
\CODE
        REAL FUNCTION F( X, Y )
        REAL X, Y(:), B(I)
        !HPF$ ENVIRONMENT :: ON HOME(X)
        !HPF$ INHERIT Y
        !HPF$ ALIGN B(:) WITH Y(:)
        INTEGER I
        USE MODULE_DEFINING_A
        Z = 0.0
        DO I = 1, SIZE(Y)
            Z = Z + A(I)*X + B(I)*Y(I)
        END DO
        F = Z
        END
\EDOC
Assume {\tt A} is defined as a distributed, global array in module 
{\tt MODULE\_DEFINING\_A}.  
What should the {\tt RESIDENT} clause mean regarding operations in
{\tt F}?  
The expression {\tt A(I)} in the {\tt RESIDENT} directive might 
reasonably mean references only to the array {\tt A} that is visible in the 
caller, or it might mean references to any array named {\tt A}.
Note that the {\tt A} in the caller may be local, 
the same global array as the {\tt A} in {\tt F} (if the caller used
{\tt MODULE\_DEFINING\_A}), 
or a different global array (if the caller used a different module).  
Perhaps a limiting case is array {\tt B}.  
The array {\tt B} in function {\tt F} is local, and thus different from the 
caller; however, because of the restrictions on {\tt ON} clauses it is certain 
that the local {\tt B} will be mapped to the {\tt ON} processors set.
Thus, the {\tt RESIDENT} assertion is trivially true.  
To further confuse matters, {\tt RESIDENT} variables might seem to
apply to dummy arguments that become associated with those variables. 
Unfortunately, this implies that the lexical expression {\tt B} in the
caller refers to the lexical expression {\tt Y} in {\tt F}, which
stretches the definition of ``lexical'' beyond the breaking point.
For all these reasons, it was decided to limit the meaning of named
variables in {\tt RESIDENT} clauses to the lexical scope of the directive.
\end{rationale}

\item If the {\tt RESIDENT} directive does not contain a {\it
local-var-list}, then the directive asserts that all references in the
caller {\em and the called procedures\/} are local as defined above.  
For example, consider the statements:
\CODE
        !HPF$ RESIDENT
        A(I) = F( A(I), B(LO:HI) )
\EDOC
The directive declares all variable refences in the statement
(including the actual parameters) to be local to the current {\tt ON}
processor set, and that {\tt F} itself does not reference or update
any nonlocal variables.

\begin{rationale}
The {\tt RESIDENT} assertion is always true for data local to the called 
procedure.  This is true because the called procedure must use a 
declarative {\tt ON} clause, which in turn limits the set of
processors that can store any local explicitly mapped variables.  
The above definition extends 
this assertion to all global explicitly mapped data, producing a very 
powerful directive.  
This is similar to the meaning of {\tt INDEPENDENT}, in that 
it also makes an assertion about variable accesses in any called procedure 
in the loop.  
An alternative semantics for {\tt RESIDENT} would have been to 
avoid propagating the assertion interprocedurally (i.e.  treat both the 
variable-list version and the no-list version the same).  However, this 
would not provide enough information to optimize code on certain machines.  
In particular, it would have made task parallelism quite difficult on 
message-passing machines.
\end{rationale}

\end{itemize}
          
\begin{implementors}
{\tt RESIDENT} without a variable list guarantees that no one-sided 
communication outside of the {\tt ON} processor set will be generated by the 
callee.  Such a procedure can be called only on the ``active'' processors, 
unless the runtime system has additional constraints (for example, if the 
runtime system requires all processors to participate in collective 
communications).

The other forms of {\tt RESIDENT} provide information that could be propagated 
interprocedurally.  
For example, if the actual argument to a subprogram is asserted to
be {\tt RESIDENT} and is passed transcriptively, then anything that is
{\tt ALIGN}ed to it in the callee will also be {\tt RESIDENT}.
If the information is not propagated, the only result 
will be less optimization.
\end{implementors}

\begin{users}
Although the {\tt RESIDENT} assertion applies interprocedurally, it is by no 
means certain that all compilers will make use of this information.  In 
particular, separate compilation limits the propagation that can take 
place.  
It is therefore good practice to include a {\tt RESIDENT} clause 
both in the caller's {\tt ON} directive and in the callee. 
(This assumes that the assertion is true, of course!)
This ensures that the compiler has the {\tt RESIDENT} information
available when it is compiling both ends of the procedure call.  
This is especially useful for {\tt RESIDENT} clauses without a
variable list; knowing that all data accessed is local allows many
optimizations that are not otherwise possible. 
\end{users}



\subsection{Examples of RESIDENT Directives}
\label{sub-res-exapmles}

As in Section~\ref{sub-on-examples}, our aim here is to suggest idioms
that may be generally useful to programmers.  We begin by expanding on
two earlier examples.

{\tt RESIDENT} is most useful in cases where the compiler cannot
detect access patterns.  Often this arises due to the use of
indirection, as in the following examples:
\CODE
        REAL X(N), Y(N)
        INTEGER IX1(M), IX2(M)
        !HPF$ PROCESSORS P(NP)
        !HPF$ DISTRIBUTE (BLOCK) ONTO P :: X, Y
        !HPF$ DISTRIBUTE (BLOCK) ONTO P :: IX, IY
        
        !HPF$ INDEPENDENT
        DO I = 1, N
          !HPF$ ON HOME( X(I) ), RESIDENT( Y(IX(I)) )
          X(I) = Y(IX(I)) - Y(IY(I))
        END DO
        
        !HPF$ INDEPENDENT
        DO J = 1, N
          !HPF$ ON HOME( IX(J) ), RESIDENT( Y )
          X(J) = Y(IX(J)) - Y(IY(J))
        END DO

        !HPF$ INDEPENDENT
        DO K = 1, N
          !HPF$ ON HOME( X(IX(K)) ), RESIDENT( X(K) )
          X(K) = Y(IX(K)) - Y(IY(K))
        END DO
\EDOC

As we saw in Section~\ref{sub-on-examples}, {\tt X(I)} is always local
in the {\tt I} loop and {\tt IX(I)} and {\tt IY(I)} rarely are.
The {\tt RESIDENT} directive above ensures that {\tt Y(IX(I))} is
local as well.  This would most likely be due to some property of the
algorithm that generated {\tt IX} (for example, if {\tt IX(I)=I} for
all {\tt I}).  
Note that it is possible for an expression (e.g. {\tt Y(IX(I))}) to be
local even though one of its subexpressions ({\tt IX(I)}) is not.

The directive gives no information about {\tt
Y(IY(I))}; it might have only one nonlocal value, or all its values
might be nonlocal.  (We assume that if there were no nonlocal values,
then the {\tt RESIDENT} clause would include {\tt Y(IY(I))} as well.)
If there are many local elements referenced by this expression, and
they can easily be separated from the local elements, then it may be
worthwhile to restructure the loop to make this clear to the compiler.
For example, suppose that we knew that only the ``first'' and ``last''
{\tt X} elements on each processor were nonlocal.  The loop could then
be split thus:
\CODE
        !HPF$ INDEPENDENT, NEW(LOCALI)
        DO I = 1, N
          !HPF$ ON HOME( X(I) ), RESIDENT( Y(IX(I)), Y(IY(I)) ) BEGIN
            LOCALI = MOD(I,N/NP)
            IF (LOCALI\=1 .AND. LOCALI\=0) THEN
              X(I) = Y(IX(I)) - Y(IY(I))
            END IF
          !HPF$ END BEGIN
        END DO
        !HPF$ INDEPENDENT, NEW(LOCALI)
        DO I = 1, NP
          !HPF$ ON (P(I)), RESIDENT( X(LOCALI), Y(IX(LOCALI)) ) BEGIN
            LOCALI = (I-1)*N/NP
            X(LOCALI) = Y(IX(LOCALI)) - Y(IY(LOCALI))
            LOCALI = I*N/NP
            X(LOCALI) = Y(IX(LOCALI)) - Y(IY(LOCALI))
          !HPF$ END BEGIN
        END DO
\EDOC
The first loop (inefficiently) processes the local elements of {\tt
Y(IY(I))}, while the second (more efficiently) handles the rest.  On
most machines, it would pay to rewrite both loops to avoid the
division operations, for example by creating a logical mask {\em a priori}.

In the {\tt J} loop, the {\tt RESIDENT} clause asserts that all
accessed elements of {\tt Y} are local.  In this case, that is
equivalent to the assertion
\CODE
        !HPF$ RESIDENT( Y(IX(J)), Y(IY(J)) )
\EDOC
Although the original {\tt RESIDENT} clause only referred to the
lexical expression {\tt Y}, the compiler can infer that the
subexpressions are also local.  This is because it is impossible for a
subobject to be on a different processor than the ``parent'' object
is.  This observation can often shorten {\tt RESIDENT} clauses
substantially.

In the {\tt K} loop, the following references are local:
\begin{itemize}
\item {\tt Y(IX(K))}, because {\tt Y} has the same distribution as 
        {\tt X} and {\tt X(IX(K))} is local (due to the {\tt ON} clause).
\item {\tt X(K)}, because of the {\tt RESIDENT} clause.
\end{itemize}
Note that a reference may be local even if it does not appear
explicitly in a {\tt RESIDENT} clause.  One mark of a good compiler
will be that it aggressively identifies these elements.


Locality information is particularly critical interprocedurally.
Here, the {\tt RESIDENT} directive without a {\it local-var-list\/}
can be used to good advantage.  Consider the following extension of
the block-structured example from Section~\ref{sub-on-subr}:
\CODE
        !HPF$ PROCESSORS PROCS(NP)
        !HPF$ DISTRIBUTE X(BLOCK) ONTO PROCS

        ! Compute ILO(IP) = lower bound on PROCS(IP)
        ! Compute IHI(IP) = upper bound on PROCS(IP)
        DONE = .FALSE.
        DO WHILE (.NOT. DONE)
          !HPF$ INDEPENDENT
          DO IP = 1, NP
            !HPF$ ON (PROCS(IP)), RESIDENT
            CALL SOLVE_SUBDOMAIN( IP, X(ILO(IP):IHI(IP)) )
          END DO
          !HPF$ ON HOME(X) BEGIN
            CALL SOLVE_BOUNDARIES( X, ILO(1:NP), IHI(1:NP) )
            !HPF$ RESIDENT
            DONE = CONVERGENCE_TEST( X, ILO(1:NP), IHI(1:NP) )
          !HPF$ END BEGIN
        END DO
\EDOC
Recall that the {\tt INDEPENDENT} {\tt IP}
loop performs a computation on each subdomain's interior, where a
subdomain is mapped to a particular processor.  
The first {\tt RESIDENT} clause additionally informs the compiler that no
subdomain uses data from another processor.
Without this information, the compiler would have to assume a
worst-case scenario in which each subdomain performed its updates
based on non-local read-only data.  Any nonlocal data could not be
written by another processor without violating the {tt INDEPENDENT}
directive; however, if the data were not updated (for example, a large
lookup table) it could be stored remotely.  Particularly on
nonshared-memory machines, access to this remote data would be
difficult.  The {\tt RESIDENT} clause ensures that this possibility
need not be considered.  All data required by {\tt SOLVE\_SUBDOMAIN}
is stored locally.
The second {\tt RESIDENT} clause asserts that all data for {\tt
CONVERGENCE\_TEST} is stored on the same processors that store {\tt
X}.  The same cannot be said for {\tt SOLVE\_BOUNDARIES}, which does
not fall in the scope of the {\tt RESIDENT} directive.
For example, there might be a processors arrangement other than {\tt
PROCS} with necessary data.
Accessing this data might well cause a bottleneck in the computation
as described above.

Again, note the usefulness of {\tt RESIDENT} clauses in giving the compiler 
information.  Few compilers would be able to unravel nontrivial assignments 
to ILO and IHI, and no current compiler would even attempt to understand 
the comments in the above code fragment.
End of advice to programmers.



Because it is an assertion of act, the compiler can draw many inferences 
from a single {\tt RESIDENT} clause.  For example, consider the following case:
\CODE
        !HPF$ ALIGN Y(I) WITH X(I)
        !HPF$ ALIGN Z(J) WITH X(J+1)
        
        !HPF$ ON HOME( X(K) ), RESIDENT( X(INDX(K)) )
        X(K) = X(INDX(K)) + Y(INDX(K)) + Z(INDX(K))
\EDOC
The compiler is justified in making the following assumptions in compiling 
the assignment statement (assuming it honors both the ALIGN directives and 
the {\tt ON} directive):
\begin{itemize}
\item {\tt X(K)} requires no communication (because of the {\tt HOME} clause)
\item {\tt X(INDX(K))} requires no communication (because of the 
{\tt RESIDENT} clause)
\item {\tt Y(INDX(K))} requires no communication (because {\tt Y} 
has the same mapping as {\tt X}, and {\tt INDX(K)} clearly cannot change 
values between its use in the two references {\tt X(INDX(K))} and 
{\tt Y(INDX(K)))}
\end{itemize}
The compiler cannot make any assumption about {\tt INDX(K)} or 
{\tt Z(INDX(K))} from 
the above code.  There is no indication how {\tt INDX} is mapped relative 
to {\tt X}, 
so the {\tt ON} directive gives no guidance.  Note that the fact that an 
expression (here, {\tt X(INDX(K))}) is local does not imply that its 
subexpressions (here, {\tt INDX(K)}) are also local.  
Similarly, {\tt Z}'s mapping does 
not determine if {\tt Z(INDX(K))} would be local; it indicates that 
{\tt Z(INDX(K)-1)}
is local, but that isn't a great help.  If the compiler has additional 
information (for example, {\tt X} is distributed by {\tt BLOCK} and 
{\tt INDX(K)} is not near 
a block boundary), it might be able to make additional deductions.

\begin{implementors}
One mark of a good compiler will be that it aggressively propagates 
{\tt RESIDENT} 
assertions.  This is likely to significantly reduce communication costs.  
Note the cases under "Advice to users" below.
\end{implementors}

\begin{users}
One can expect compilers to differ in how aggressive they are in drawing 
these deductions.  Higher-quality compilers will be able to identify more 
references as local, and use this information to eliminate data movement.  
All compilers should recognize that if an element of one array is local, 
then the same element of any other arrays with the same static mapping 
(i.e.  arrays {\tt ALIGN}ed together, or with the same {\tt DISTRIBUTE}
pattern and array size) will also be local.  
That is, any compiler should recognize 
{\tt Y(INDX(K))} in the above example as local.  Dynamically changing array 
mappings (i.e. {\tt REALIGN} and {\tt REDISTRIBUTE}) will tend to limit such 
information and information propagation.  Also, assignments that might 
change subexpressions (for example, an assignment to {\tt K} or any element of 
{\tt INDX} in the above example) will force the compiler to be conservative in 
its deductions.
\end{users}


\section{The TASK\_REGION Directive}
\label{sec-tasking}

Task parallelism is expressed implicitly in HPF by mapping data 
objects onto subsets of processors and adding assertions that
allow concurrent execution of different  code blocks on different
processor subsets. A data objects is mapped to a processor subset
by distribution onto a 
subsection of a processor arrangement.
Execution on a subset of processors is specified by using an 
{\tt ON} directive. This section introduces a {\tt TASK\_REGION}
directive that allows the user to implicitly specify that
disjoint processor subsets can execute blocks of code concurrently.
  
A {\tt TASK\_REGION} construct is used to assert that a block of code 
satisfies the following set of constraints.
 All lexically outermost {\tt ON} blocks
inside a task region must have a {\tt RESIDENT} attribute
implying that all  data accessed inside them is mapped to the
corresponding processor subset. Further,
the code inside two such {\tt ON} blocks must not have interfering
I/O. Under these constraints, two such {\tt ON} blocks  
 can safely execute concurrently if they execute on disjoint
processor subsets.

\subsection{Syntax of the TASK\_REGION Directive}

%[CHUCK : Could  you replace this with a BNF - I suspect
% it will take  you 5 mins and will take me much longer]

A task region is a single entry region delimited by:
\CODE
!HPF$ TASK REGION
  ......
!HPF$ END TASK REGION
\EDOC


\subsection{Semantics of the TASK\_REGION Directive}

The task region directive is a way for the programmer to assert
that a section of code satisfies a set of conditions. The compiler
is expected to use these assertions to generate task parallel code.
We will refer to a block of code enclosed by a 
{\tt TASK\_REGION ... END TASK\_REGION} pair as a ``task region''.

A task region can contain blocks of code that are directed to execute {\tt ON} 
processor subsets.  All other code executes on a subset that 
contains all executing processors.  Every {\tt ON} block at the outermost
nesting level (i.e.  not inside another {\tt ON} block or another task 
region) inside a 
task region is defined as a ``lexical task''.  Every execution instance of 
a lexical task is defined as an ``execution task'' and will also be
referred to
as just ``task'' when the distinction is clear from the context.

The following restrictions must hold  inside a task region:  
\begin{itemize}
\item Every {\tt ON} block corresponding to a lexical task must
have the {\tt RESIDENT} attribute.
This means that, for  reading a variable inside an execution task,
the executing processor subset for the task 
(also referred to as {\em active processors}) 
must own at least one copy of the variable, and for writing, they must own 
all copies of that variable.

\item An I/O operation inside an
execution task may interfere with an I/O operation inside
another execution task if and only if the two tasks execute on
identical subsets of  processors. Note that  two execution tasks
can be  instances of the same or different lexical tasks.
In general, two I/O operations interfere if they access the same
file or unit. The conditions for interference of I/O operations are
detailed in Section~\ref{sub-independent} in the context of the
{\tt INDEPENDENT} directive.

\end{itemize}

\subsection{Execution Model and Usage}

A task region does not introduce a fundamentally new execution model.  
However, the asssertions implicit in a task region imply that only
the specified executing processors of an execution task need to
participate in its execution, and that other processors can skip its
execution.  A processor executing a task 
region participates in the execution of all tasks
executing on a processor subset that it belongs to and
does not participate in the  execution of tasks executing 
on processor subsets that it does not belong to. 
Code outside lexical tasks is 
executed as normal data parallel code by all processors.  The access 
restrictions for a task region guarantee that the results obtained
by this execution paradigm will be consistent with pure data
parallel execution of a task region.

A task region presents a simple yet powerful model to write integrated
task and data parallel programs. We illustrate three basic computation
structures in which task parallelism can be effectively exploited
with this model.

\begin{enumerate}

\item {\em Parallel sections:} 
A task region can be used to divide the available processors into 
disjoint sets for performing independent computations, simulating
what is often referred to as {\em parallel sections}. This form of
task parallelism is relatively straightforward and useful in many
application scenarios, an example being multiblock applications.
The task region simply contains
a sequence of {\tt RESIDENT ON} blocks on disjoint processor subsets. 
Note that the division of processors among subsets can be dynamic,
that is, it can be in terms of other variables computed during execution.

\item {\em Nested parallelism:}
Task regions can be nested, and in particular, a subroutine call made
from an execution task can further subdivide the executing (or active)
processors using another task region directive. This allows the exploitation
of nested parallelism. An example is the implementation of
dynamic tree structured divide and conquer computations. As a 
specific example,
{\em quicksort} can be implemented by  recursively 
partitioning the input array of keys 
around a pivot and  assigning proportionate number of processors
to the two new arrays obtained as a result of partitioning.

\item {\em  Data parallel pipelines:}
Task regions can be used to implement 
pipelined data parallel computations. We will
illustrate this with a 2 dimensional fast Fourier transform (2D FFT)
computation. The first stage of a 2D FFT reads a two dimensional matrix
and performs a 1 dimensional FFT on each row of the matrix. The second
stage performs a 1 dimensional FFT on each column of the matrix and generates
the final output. In a pipelined data parallel implementation of this
form of 2D FFT, the two stages are mapped on to disjoint subsets of processors.
Task and data parallel code for a 2D FFT, along with a brief
description, is included in Section~\ref{sec:2DFFT}.

\end{enumerate}

\subsection{Implementation}
A task region is simply an assertion about a code block and the
exploitation of task parallelism is at least partially dependent
on the compilation scheme. While the specifics of how task parallelism
is exploited will be strongly dependent on the parallel system
architecture, the compiler, and the  underlying communication 
model, we will point out some  important considerations and
illustrate task parallel code generation with an example. We primarily
address distributed memory machines using a  message passing 
communication and synchronization model, but will point out
some of the important issues relating to shared memory implementations.


\subsubsection{Localized computation and communication}
It is of central importance that computation and communication
inside an executing task should not  involve any processors
other than those directed to execute the task in the
relevant {\tt ON} clause.

On entry to a lexical task, the compiler has to insert checks so
that the processors not in the relevant subset jump to the code
following the task. Since an execution task cannot access data
outside of the active executing processor subset, no communication
needs to be generated between the relevant executing processors
and other processors. In a message passing model, a communication
generation algorithm that only generates necessary messages will
naturally achieve the desired results. However, some communication
schemes can involve generation of empty messages between processors
that do not communicate and it is important to ensure that empty
messages are not generated between active processors of an executing
task and other processors.

A communication model that uses barriers for synchronization (in
shared or distributed memory machines) must ensure that all barriers
inside an executing task are subset barriers that only span the 
active processors. An implementations may also need to include a
subset barrier on entry and exit to an executing task for consistency
of data accesses inside and outside an executing task. In general,
the compilation framework has to ensure the consistency of data
accesses inside and and outside an executing tasks and this can be done
in the context of  virtually any synchronization scheme in a shared
or distributed memory environment.



\subsubsection{Replicated computations}
All computations exclusively involving replicated variables should be 
replicated on all executing processors.
A simple alternative is that  one processor performs the
computation and broadcasts the results to all processors. While such
replication
is generally profitable in HPF anyway, it has additional importance
in a task region since the communication generated by a broadcast can
cause additional synchronization that may interfere with
task parallelism.

\subsubsection{Implications for I/O}
In some parallel system implementations, I/O is performed through
a single node of the system. Task parallelism in the presence of 
I/O assumes that all nodes can perform I/O independently and this
paradigm has to be supported, although it is not necessary that 
each node be able to physically perform all I/O operations independently.
One simple solution is to have a single
designated I/O processor that performs
all I/O but is not considered an executing processor and hence does 
not have any execution related dependences.

\subsubsection{SPMD or MIMD code generation}
Another issue for the compiler is whether or not the same code image
should execute on all processors. Since different processor groups 
may need different variables, a naive SPMD implementation is likely
to be wasteful of memory since it must allocate all variables on
all processors. This can be addressed by dynamic memory allocation,
but at the cost of added complexity. Using different code images for
different processor subsets is another solution which leads to
significant added complexity.

\subsection{Example: 2-D FFT}
\label{sec:2DFFT}

This sections shows the use of task parallelism to build
a pipelined data-parallel 2-dimensional FFT and illustrates 
the compilation of task parallelism by  showing
SPMD code generated from the HPF program.

The basic  sequential 2DFFT code is as follows:
\CODE
      REAL, DIMENSION(n,n) :: a1, a2

      DO WHILE(.true.)
          READ (unit = 1, end = 100) a1
          CALL rowffts(a1)
          a2 = a1
          CALL colffts(a2)
          WRITE (unit = 2) a2
          CYCLE
100       CONTINUE
          EXIT
      ENDDO
\EDOC


To write a pipelined task and data parallel 2D FFT
in HPF, the code is slightly modified and several HPF
directives are added.
First,  variables {\tt a1} and {\tt a2} are distributed onto disjoint
subsets of processors, and then a task region is used to create two
lexical tasks to do {\tt rowffts}  and {\tt colffts} on different
subsets of processors. The assignment {\tt a2 = a1} in the task region
specifies transfer of data between the tasks. A new variable {\tt done1}
is introduced to store the termination condition.
The modified code is as follows:

\CODE
        REAL DIMENSION(n,n) :: a1,a2
        LOGICAL done1
!HPF$   PROCESSORS procs(8) 

!HPF$   DISTRIBUTE a1(block,*) ONTO procs(1:4)
!HPF$   DISTRIBUTE a2(*,block) ONTO procs(5:8)

!HPF$   TEMPLATE, DIMENSION(4), DISTRIBUTE(BLOCK) ONTO procs(1:4) :: td1
!HPF$   ALIGN WITH td1(*) :: done1
                 
!HPF$   TASK REGION
        done1 = .false.
        DO WHILE (.true.)
!HPF$       ON HOME(procs(1:4)) BEGIN, RESIDENT
              READ (unit = iu,end=100) a1
              CALL rowffts(a1)
              GOTO 101
    100       done1 = .true.
    101       CONTINUE
!HPF$       END ON
            
            IF (done1) EXIT
            a2 = a1

!HPF$       ON HOME(procs(5:8)) BEGIN, RESIDENT
               CALL colffts(a2)
               WRITE(unit = ou) a2
!HPF$       END ON
        ENDDO
!HPF$   END TASK REGION
\EDOC


Finally, we show simplified SPMD code generated
for each processor. We assume
a  message passing model where sends are asynchronous and nonblocking
and receives block until the data is available. We use a simple memory
model where variable declarations are identical across
all processors even though some variables will be referenced only on
subsets of the processors.
A shadow variable {\tt done1\_copy} is created by the compiler to
transfer information from processor subset 1 to processor subset 2
about termination of processing. The code is as follows:


\CODE
        REAL DIMENSION(n/4,n) :: a1, a2
        BOOLEAN done1

C       Following are compiler generated variables       
        BOOLEAN done1_copy
        BOOLEAN inset1, inset2

C     
C       Following magic compiler function call is to set the variables
C       inset1 and  inset2 to .true. for subset1 and subset 2 processors
C       respectively, and .false. otherwise.
C
        CALL intialize_tasksets(inset1,inset2)

C       Code for processor subset 1
        IF (inset1)
           done1 = .false.
           DO WHILE (.true.)
              READ (unit = 1,end=100) a1
              CALL rowffts(a1)
              GOTO 101
    100       done1 = .true.
    101       CONTINUE
              _send(done1,procs(5:8))
              IF (done1) EXIT
              _send(a1,proces(5:8))
           ENDDO
         ENDIF

C       Code for processor subset 2
        IF (inset2)       
           DO WHILE(.true.)
              _receive(done1_copy,procs(1:4))
              IF (local_done1) EXIT
              _receive(a2,procs(1:4))
              CALL colffts(a2)
              WRITE (unit = 2) a2
           ENDDO
        ENDIF
\EDOC

{\tt \_send} and {\tt \_receive} are  communication calls to
transfer variables between subsets of processors. Program execution
until the end of input is as follows.
Subset 1 processors repeatedly read input, compute
{\tt rowffts}, and send the computed output as well as {\tt done1} flag
(which is not set) to subset 2 processors. The subset 2 processors
receive the flag and the data set, compute
{\tt colffts} and write the results to the output. When the end of input is
reached, subset 1 processors set the flag {\tt done1} , send it and terminate
execution. Subset 2 processors receive the flag, recognise that the end of
input has been reached, and terminate execution.
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Date: Thu, 29 Aug 1996 15:31:20 -0700 (PDT)
From: "Scott B. Baden" <baden@cs.ucsd.edu>
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I've cleaned this up a bit and also brought
it in line with Extrinsic Approved Extension chapter.

Scott
% File: spmd-to-hpf-ext.tex

% Contents:
% Proposed Extension for SPMD interface to HPF  for HPF 2.0 document

% Revision history:
% Aug-8-96	Created by Scott B. Baden, UCSD
% Aug-15-96	Scott B. Baden, UCSD
% Aug-29-96	Scott B. Baden, UCSD


\chapter{Proposed Extension for SPMD calling HPF}
\label{ch-spmd-hpf}

{\em
Comments on this chapter should be directed to 
Scott Baden ({\tt baden@cs.ucsd.edu})
and {\tt hpff-doc@cs.rice.edu}.
Please use ``{\tt Comments on SPMD-to-HPF}'' as the {\tt Subject:}
line.
\par
}


\newcommand{\PROCS}  {{\tt PROCESSORS} }
\newcommand{\HPFINIT}  {{\tt HPF\_INIT} }
\newcommand{\HPFLOCAL}  {{\tt EXTRINSIC(HPF\_LOCAL)}}
\newcommand{\MAD}  {{\tt MAD}}
\newcommand{\CPP}  {{\tt C++}}
\newcommand{\MA}  {{\tt MAPPED\_ARRAY}}
\newcommand{\TMA}  {{\tt TO\_MAPPED\_ARRAY}}
\newcommand{\TOLOCAL}  {{\tt TO\_LOCAL}}
\newcommand{\offset}[1]{\begin{center} \tt #1 \end{center}} 

% ******************** Start of Document ********************

\section{SPMD Coordination of HPF}
\label{f90-locals}


The current HPF standard does not address the problem of
coordinating the concurrent execution of multiple HPF
procedure invocations, nor their interaction via
an SPMD harness written in an extrinsic language such as \CPP.
We propose an interface for
coordinating concurrently executing HPF procedures from an extrinsic SPMD layer.
This interface requires neither language extensions nor new language
features, and requires only a handful of library entries
that access the HPF run time system.
The proposed interface is language-independent.  It enables
inter-operability between software components developed in different
languages.

Note: Chuck Koelbel and Joel Saltz assisted in the development of this
proposal.


\section{Programming Model}
Our model comprises multiple HPF invocations that interact
with each other concurrently.
Separate HPF invocations will be orchestrated
via an  SMPD program, and
may or may not involve the identical code.
HPF invocations will import scalars and global arrays allocated from 
the SMPD  program.
The primary concern here in how to
deal with global arrays.

The SPMD code which controls the
interaction of multiple HPF invocations
may be   written in \HPFLOCAL\ or another
extrinsic language, e.g. \CPP.  We will use \HPFLOCAL\ here.
Other possibilities include multiple HPF programs that communicate
by calling an extrinsic SPMD program, which have been
addressed elsewhere in this document.
The discussions in this chapter
augment those outlined in the \HPFLOCAL\ interface with extensions
that may facilitate coordination via extrinsic languages like \CPP.


\section{The Interface}

Our proposed interface
specifies the interaction of an SPMD program, written
in an extrinsic language,  that calls HPF.
The interface supports the allocation of, and access to,
HPF global arrays from the SPMD coordinating code.
SPMD code views
each HPF global array as an entity called
a {\em mapped array} which will refer to as a \MA.

\subsection{Mapped Arrays}
It is assumed that the HPF compiler translates a call to an HPF
entry as follows.  First, an implementation-specific {\em name-mangling}
rule is applied to the entry name to conform with linkage conventions.
Second, each global array argument is converted to a \MA\
argument.  (Scalars are passed unchanged.)
The conversion process in implementation-dependent.
For example, some implementations convert each global array argument
into a pair of arguments: a
{\em mapped array descriptor} or \MAD\, and a pointer to
the start of the local storage for the mapped array.  In this case two
arguments would actually be passed for each mapped array argument,
though the number and representation of these arguments is generally
implementation-dependent.

By an abuse of notation we will refer to a mapped array reference
as if it were a reference to value of a distinguished type \MA.
While no such type may in fact  exist, the notation simplifies the
ensuing discussions.
We will employ the notation \TMA{\tt (A)} to
designate the desired conversion of global array argument {\tt A}
to a reference of (the fictitious) type \MA.
Thus, an argument of the form 
\TMA{\tt (A)}
is understood to represent the \(k>1\) actual parameters, which
might, for example,
contain a corresponding \MAD\ and starting address.
Similarly a declaration of the form
\offset{MAPPED\_ARRAY(A)} is understood to
declare \(k>1\) variables;  in the above example, there would
be one declaration for the \MAD,
another for the starting address to the corresponding local data.


As described below,
the interface includes various
entries for querying and manipulating \MA.
This interface should be packaged as a module
as described at the end of this chapter.
This module must be {\tt USEd} in all program source files
that employ the proposed interface.

\subsection{SPMD Execution}

This proposal defines a  language-independent
interface consisting of a set of
entries that enables SPMD code
written in an extrinsic language to communicate with HPF.
Interfaces for  other extrinsic languages,
e.g. C are out of the scope of this document.

We define SPMD execution as follows.  An SPMD program
executes on a {\em process group}.
We identify
an HPF \PROCS\  arrangement with  a process group, and employ
an opaque object called 
a {\em communicator} (as in MPI) to  specify the  group's membership.
The advantage of this approach is that the values returned by
{\tt NUMBER\_OF\_PROCESSORS} and {\tt PROCESSORS\_SHAPE} are well-defined,
as are collective communication operations.
%Note that it is possible to dynamically change the members of a process
%group or to change the group's topology by modifying
%attributes of the
%communicator.
Each process will be considered a physical processor by the HPF code.  The
called HPF program will have access to members of the process group.
It will not, however, have direct
access to processes outside that group.

All members
of a process group execute the same program in loosely synchronous
fashion, collectively 
making calls to HPF procedures (including those defined by
the proposed interface)
{\em as if\ } at the same time.
(Calls to HPF from SPMD may or may not need to be explicitly synchronized
at a barrier.)
As far as the HPF procedure is concerned, it will
not know
the origin of the argument, which could have in fact originated from
another HPF program.  It follows that
the SPMD program is responsible for passing mapped arrays to an HPF
procedure in conformance  with the procedure's expectations, i.e. the distribution
must match and so on. All invocations of HPF procedures
in the process group must pass the same \MA\ in each corresponding position
of the argument list (remembering that the accompanying local data
will be generally be different for each invocation.)
Scalar arguments must be consistent among
all members of the process group.


\begin{implementors}
Implementation of the ``HPF-from-extrinsic'' interface will be
facilitated with MPI.
However, implementors are free
to  employ their own implementation strategy.
Implementors who do not employ MPI 
need a mechanism for defining groups of processors that
only talk to each other; non-MPI implementations will obviously treat
these
differently from MPI ones.

The use of the proposed interface will be simplified by the provision
of a macro called \TMA, to
translate an HPF
global array reference to a \MA, containing, in our above
example, an appropriately formed
\MAD\ and the start of a local data area.
\end{implementors}

\subsection{HPF Run Time Initialization}

A call to a procedure \HPFINIT\ is required to establish
various state needed by the HPF run time system, that will, for
example, enable,
the processor to determine `who it is.'
\HPFINIT\ must   be passed a communicator corresponding
to the process group used to invoke the HPF program(s).
Successive calls to \HPFINIT\ may be used to set up alternative
\PROCS\ topologies or as required to invoke HPF code
on different processor groups.

\begin{implementors}
\HPFINIT\ should extract the \PROCS\ topology from the communicator
passed into it.

A mechanism is required for managing MPI-style communicators;
either MPI will be available from the SPMD program, or the
implementor must provide equivalent functionality.
\end{implementors}

Two or more HPF invocations may be simultaneously active if they execute on
different communicators with disjoint process groups.
To achieve this, the individual groups each define their own communicator.
The separate communicators are then used by \HPFINIT\
to establish the communication domains.

To handle multiple HPF invocations across different
processing groups, the SPMD coordinating code  may need to
explicitly query each processor  for membership within the desired communicator.
For example, if we are invoking procedures {\tt A1, A2}
on one processor group, and procedure {\tt B} on another, then
we employ the following:
\begin{verbatim}
!     Set up the processor groups
      call HPF_INIT(GroupA, ...)
      call HPF_INIT(GroupB, ...)

!     isMember( ) determines membership within the respective communicators
      if ( isMember(GroupA)) then
          call A1(...)      
          call A2(...)
      else if ( isMember(GroupB)) then
          call B(....)     
      end if
\end{verbatim}


HPF programs associated with overlapping communicators can also be defined,
but require additional system support to execute in parallel.  (In effect,
the underlying system must allow multi-threading to allow the process(es) in
the overlap to participate in both HPF programs at once.)  Such support may
be desirable, but is not mandated by this proposal.
Overlapping communicators could, however, be useful in different phases.
For example, one phase might use 8 processes, followed by another phase
using only 4.  The programmer could accomplish this by creating an
8-process communicator and a 4-processes communicator with a subset of the
processes.  \HPFINIT\ would have to be called to establish
the communicator for each phase to alert
the HPF runtime that a different communicator was in use.

Regardless of how the communicators are set up, an HPF procedure has
access only to the process group associated with the communicator in the
last executed \HPFINIT\ call.
This allows us to define {\tt NUMBER\_OF\_PROCESSORS} to return the number
of processes in that communicator, and similarly make consistent
definitions for the other HPF inquiry procedures.
It follows that
SPMD code must invoke an HPF procedure on {\em exactly}
those processors in the intended processor group---no more an no less.
This will likely be supported by a conditional statement which
will determine membership within the respective communication domains
established by SPMD program.

Note that physical processors in different communicators may
return different values for {\tt NUMBER\_OF\_PROCESSORS}, but they cannot
be executing the same instantiation of an HPF procedure.
This implies that
actual arguments to an HPF procedure must all be allocated
from the same process group,
and that data motion between mapped arrays allocated to different
process groups must be handled at the SPMD level.
(MPI's inter-communicators allow precisely
this sort of communication.)
We restrict global data accessed in the HPF procedure
in the same way.


\subsection{Global Array Allocation From SPMD}

The functionality required to support extrinsic SPMD coordination of HPF
invocations centers on the ability to allocate, from the SPMD level, global
(mapped)
HPF arrays with a specified \PROCS\ arrangement, alignment,
and decomposition.  In the interest of simplicity, allocation
will be restricted as follows.
\begin{enumerate}
\item Only arrays of builtin types are permitted, i.e. arrays
of derived types are excluded.

\item Only {\tt BLOCK, *, CYCLIC, } and {\tt CYCLIC(K)}
decompositions are permitted.

\item Only the  identity alignment is permitted.  Identically
aligned arrays must have the same rank and extents.
\end{enumerate}


A process group dynamically allocates a mapped array using the call

\noindent
\subsubsection*{alloc\_mapped\_arrayTTT(A, NDIM, EXTENTS, DECOMP, [ALIGN])}

\begin{tabular}{ll}
{\bf OUT} A &         a MAPPED\_ARRAY \\
{\bf IN} NDIM & number of dimensions \\
{\bf IN} EXTENTS & extents of the indices of the array  ({\tt 2*NDIM} entries) \\
{\bf IN} DECOMP & decomposition ({\tt NDIM} entries) \\
{\bf IN} ALIGN & a previously allocated \MA\ (optional) \\
\end{tabular}
\vspace{0.1in}


\noindent
{\tt TTT} is one of 5 builtin HPF types:
\offset{REAL, DOUBLE PRECISION, COMPLEX, DOUBLE PRECISION COMPLEX, INTEGER.}

The first
argument actually refers to the global array to be allocated by HPF.
The {\tt NDIM} and {\tt EXTENT} arguments
specify the number  and extent of the array axes, the {\tt DECOMP}
argument their decomposition across processors.  Each element
of {\tt DECOMP}  must be one of the following predefined names:
\offset{SERIAL, BLOCK, CYCLIC, CYCLIC(K)}

\noindent
where {\tt CYCLIC(K)} will be mapped onto distinct values for 
distinct values of {\tt K.}

The final argument is optional; it is specifies an existing array
to which the newly-allocated array will be aligned.
Such allocations are restricted to identity alignments only;
the {\tt NDIM, EXTENTS,} and {\tt DECOMP} specifications must
also be identical as well.


\subsection{Data Access}

The extrinsic SPMD layer may access a global array through a
\MA\ reference.
The interface  does not permit direct access
to the \MA, however,
since manufacturers need flexibility in representing a mapped
array.
Rather, it treats a \MA\ as an opaque object, and provides
primitives to
query the global array---e.g.
determine global shape, local shape, decomposition, and so on---or
to modify it.

The SPMD programmer has two means of accessing a mapped
array. The first way is  via the \HPFLOCAL\ interface, which 
permits access to various descriptive information
and to local data.  The second way is through
a new set of primitives that perform global copying, and may
be used to access non-local data.  

\subsubsection{Local Data Access}


For local data access we use the
\HPFLOCAL\ interface (see \ref{hpf-local}), adapted as follows
for the task at hand.

\begin{enumerate}
\item All mapped HPF arrays accessible from an
SPMD procedure are logically carved
up into blocks; the SPMD process executing on a particular physical
processor sees an array containing just those elements of the global
array that are mapped to that physical processor.

\item The model assumes that array axes are mapped independently to axes of a
rectangular \PROCS\ grid, each array axis to at most one \PROCS\
axis (no ``skew" distributions) and no two array axes to the same
\PROCS\ axis.  This restriction suffices to ensure that each
physical processor contains a subset of array elements that can be
locally arranged in a rectangular configuration (of course to compute
the global indices of an element given its local indices or vice verse,
may be quite a tangled computation-- but it will be possible)



\item
The portion of a mapped array argument
in an {\tt HPF\_LOCAL} subprogram
associated with a global array dummy argument  in an HPF program
may be accessed in a block-by-block
fashion.  Library procedures such as {\tt LOCAL\_BLKCNT},
{\tt
LOCAL\_LINDEX}, and {\tt LOCAL\_UINDEX}, allow easy access to the local
storage of a particular block.
\end{enumerate}

\begin{implementors}
Random access to the elements of a mapped array is likely to be
expensive, and a separate interface described below
should be used to handle block copies.


Implementations that employ ghost cells or shadow regions may need to provide
the capability of accessing such additional data.  This proposal
does not specify how ghost cells are to be accessed or manipulated.
\end{implementors}



\subsubsection{HPF_LOCAL Primitives}
Included are\\

\begin{tabular}{lll}
{\tt GLOBAL\_ALIGNMENT} & {\tt GLOBAL\_DISTRIBUTION} & {\tt GLOBAL\_TEMPLATE } \\
{\tt GLOBAL\_LBOUND  } & {\tt GLOBAL\_UBOUND } & {\tt GLOBAL\_SHAPE  }\\
{\tt GLOBAL\_SIZE } & {\tt ABSTRACT\_TO\_PHYSICAL  } & {\tt PHYSICAL\_TO\_ABSTRACT }\\
{\tt LOCAL\_TO\_GLOBAL  } & {\tt GLOBAL\_TO\_LOCAL } & {\tt LOCAL\_BLKCNT  }\\
{\tt LOCAL\_LINDEX } & {\tt LOCAL\_UINDEX} & {\tt MY\_PROCESSOR }\\
\end{tabular}

\ \\
\noindent

In order to use the \HPFLOCAL\ interface, we need a way of converting
a \MA\ actual parameter into a form expected by
the \HPFLOCAL\ library.
To this end we define the macro \TOLOCAL, which takes
a \MA\ argument and converts it into the appropriate representation
expected by the \HPFLOCAL\ interface.
For example, we consider the
\HPFLOCAL library primitive {\tt GLOBAL\_SHAPE}.

Assuming that global array {\tt A} has been allocated by the call
\offset{alloc\_mapped\_array(TO\_MAPPED\_ARRAY(A),NDIM=2,EXTENTS=/(3,100,1,200/),...)}
then the value returned by
{\tt GLOBAL\_SHAPE(TO\_LOCAL(A))} is \VECTOR{98 200}.


\subsubsection{Global Copying }
The Interface also provides primitives for moving data
over global sets of indices.
The first primitive merely copies one array to another.

\subsubsection*{copy\_mapped\_array\_TTT(SRC, DEST)}

\begin{tabular}{r ll}
{\tt IN} & {\tt SRC} &		\MA -- source \\
{\tt OUT} & {\tt DEST} &	\MA -- destination \\
\end{tabular}

\noindent
where {\tt TTT} is one of 5 built in HPF types:
\offset{REAL, DOUBLE PRECISION, COMPLEX, DOUBLE PRECISION COMPLEX, INTEGER.}

\noindent
The source and destination descriptors may or may not  be allocated to the same
processor group.

There is also  a variant of
{\tt copy\_mapped\_arrayTTT} that copies over designated array
sections:


\subsubsection*{copy\_mapped\_array\_secTTT(SRC, DEST, S\_SECT, D\_SECT)}

\begin{tabular}{r ll}
{\tt IN} & {\tt SRC} &		\MA -- source \\
{\tt OUT} & {\tt  DEST} &		\MA -- destination  \\
{\tt IN} & {\tt S\_SECT} &		source array section specifier \\
{\tt IN} & {\tt D\_SECT} &		destination array section specifier \\
\end{tabular}

The array section specifiers are {\tt INTEGER} \(d\)-tuples
(arrays)
where \(d\) is the common rank of the arrays.
The format of these tuples is \((r_0, r_1, ..., r_{d-1}\))
where each \(r_k\) specifies the integer range of indices for axis \(k\),
i.e. the array section {\tt (3:4, 5:6)} is specified as
{\tt /(3,4, 5,6/).}


\begin{implementors}
Though the {\tt copy\_mapped\_array\_secTTT( )}
could be implemented
using the \HPFLOCAL\ interface, doing so may not to
be as efficient as taking advantage of direct access to
layout information provided by the compiler.
\end{implementors}


\subsection{Summary of what is to be provided}
In practice, multi-lingual programming  can be given only minimal
language and compiler support.
Some installation-dependent coding is
required, for example to handle name mangling, argument
passing conventions, and so on.  Such code is generally not portable.

We propose an interface that does not rely on language extensions,
yet which offers reasonable assurances of portability.
To this end,
we strongly recommend that Interfaces for SPMD applications
inter-operating with
HPF provide the following constants and entries and package
them in a 
{\tt MODULE}.  (In the
case of {\tt f77, C,} or \CPP, these would be packaged as part of
a header file, and probably contain a class definition in the case of \CPP.)
In addition, certain macros should be defined as described below to facilitate
manipulation of a \MA.

\subsubsection*{Constants}
\begin{tabular}{llll}
{\tt SERIAL} & {\tt BLOCK} & {\tt CYCLIC} & {\tt CYCLIC(K)}\\
\end{tabular}

Note: {\tt CYCLIC(K)} will probably be supported with a macro.

\subsubsection*{Library Primitives}
\begin{tabular}{ll}
{\tt HPF_INIT} & {\tt alloc\_mapped\_arrayTTT}\\
{\tt copy\_mapped\_array\_TTT} & {\tt copy\_mapped\_array\_secTTT} \\
\end{tabular}

\vspace{0.1in}
\noindent
Note: {\tt TTT} is one of 5 built in HPF types:
\offset{REAL, DOUBLE PRECISION, COMPLEX, DOUBLE PRECISION COMPLEX, INTEGER.}


\subsubsection*{Macros}
It is recommended that the macro
\TMA\ be provided to facilitate the handling of the multiplicity
of  values that comprise a \MA\ argument, and the macro \TOLOCAL\
to assist in using the \HPFLOCAL\ interface.
The macro \MA\  is recommended for declaring a value of 
type \MA, e.g.
\offset{MAPPED\_ARRAY(A)}
declares a set of variables that collectively represent
a \MA.
\section{Programming Example}


The application is to iteratively solve Poisson's equation on a
2-dimensional irregularly-shaped domain consisting of two coupled rectangular
blocks of different sizes.  The same solver is applied to each  block.  


Because the blocks have different sizes we will
allocate them to different size \PROCS\ subsets in order to balance
the workloads.  Prior to computing,
each block must furnish boundary conditions that couple
it to the other block.


\CODE
! Example illustrating coordination from an extrinsic layer
! Solve the Laplace Equation on an irregular domain using Red/Black SOR
! The computational domain consists of two squares A&B
! sitting side by side and aligned with the y axis
! Square A is m x m, Square B is n x n

extrinsic(hpf_local) program iter
!   The MAPPED_ARRAY package is part of the interface
!   It includes definitions for constants like BLOCK, SERIAL,
!   the various routines that allocate global arrays, and so on
    use MAPPED_ARRAY
!   This package specifies an HPF binding for MPI
    use MPI

!   MAPPED_ARRAY() is a macro which declares the various pieces of information
!   that make up a MAPPED_ARRAY
    MAPPED_ARRAY(A)
    MAPPED_ARRAY(B)

!   Extents of A and B
    integer, array(4) :: A_EXT = /(0,m+1,0,m+1/), B_EXT = /(0,n+1,0,n+1/)
!   Their decomposition: SERIAL corresponds to  * in HPF
    integer, array(2) :: DECOMP = /(BLOCK,SERIAL/)

    real resid, convergence
    real function smooth
    real, parameter :: EPSILON = 0.001

! Communicators
    Communicator COMM_A, COMM_B
   
!   The size of the blocks are inputs to the program
    read *, m, n

!   Allocate processors 0 to K-1  to block A, the remainder to block B
!   The value of K is determined by the relative sizes of m & n
!   ZERO_TO_KM1 and K_TO_PM1 are integer "color" arrays (i.e.  MPI)
!   specifying the  membership of each processor in the respective groups

!   Set up the process groups and communicators, one for each block
    call MPI_COMM_SPLIT(MPI_COMM_WORLD,ZERO_TO_KM1,DUMMY,COMM_A,IERROR)
    call init_HPF(COMM_A)

    call MPI_COMM_SPLIT(MPI_COMM_WORLD,K_TO_PM1,DUMMY,COMM_B,IERROR)
    call init_HPF(COMM_B)

    if (isMember(COMM_A)
!       TO_MAPPED_ARRAY( ) converts the global array reference to a
!       MAPPED_ARRAY.  k>1 arguments may correspond to TO_MAPPED_ARRAY(A)
        call alloc_mapped_arrayREAL(TO_MAPPED_ARRAY(A), 2, A_EXT, DECOMP)
    if (isMember(COMM_B)
        call alloc_mapped_arrayREAL(TO_MAPPED_ARRAY(B), 2, B_EXT, DECOMP)

    convergence = 10.0 * epsilon

    do while ( convergence < epsilon )
!       Fill in the boundary cells
        mn = min(m,n)
        I0 = /(m+1,m+1,1,mn/)
        I1 = /(m,m,1,mn/)

!       All processors in COMM_A and COMM_B must participate
!       which in this case covers all processors in MPI_COMM_WORLD
!       In a multiblock code with > 2 blocks, appropriate guards would be
!       required to restrict execution of copy_mapped_array_secTTT( ), as
!       2 communicating grids would cover only a subset of MPI_COMM_WORLD

        call copy_mapped_array_secREAL(MAPPED_ARRAY(B),MAPPED_ARRAY(A),I0,I0)
        call copy_mapped_array_secREAL(MAPPED_ARRAY(B),MAPPED_ARRAY(A),I1,I1)

!       Ensures that the global reductions are done correctly.
        residA = 0
        residB = 0

!       These calls to HPF execute in different processor groups; their
!       respective arguments were allocated with different communicators
        if (isMember(COMM_A))
            residA = smooth(A)

        if (isMember(COMM_B))
            residB = smooth(B)

!       global reduction over all processes (MPI functionality)
        call _max_scalar_REAL(residA, MPI_COMM_WORLD)
        call _max_scalar_REAL(residB, MPI_COMM_WORLD)

        convergence = amax(residA, residB)
    enddo
end program

\EDOC
\end{document}
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